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Effects of high magnetic field and substitutional doping on optical properties of cuprate superconductors

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Effects of high magnetic field and substitutional doping on optical properties of cuprate superconductors
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Liu, Hsiang-Lin, 1966-
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Thesis (Ph. D.)--University of Florida, 1997.
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Includes bibliographical references (leaves 249-267).
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Vita.
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by Hsiang-Lin Liu.

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EFFECTS OF HIGH MAGNETIC FIELD AND SUBSTITUTIONAL DOPING ON OPTICAL
PROPERTIES OF CUPRATE SUPERCONDUCTORS





By

HSIANG-LIN LIU


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY





UNIVERSITY OF FLORIDA


1997

















ACKNOWLEDGMENTS


It is my great pleasure to thank my supervisor, Professor David B. Tanner, for giving me the opportunity to be part of his research group and study a lot of very exciting projects detailed in this dissertation. His confidence and continued support are a very much valued contribution, as are the many suggestions and helpful discussions. He is also a good role model as a scientist and an educator. I will keep his attitude in mind: positive thinking, self-motivated, and enjoys working. I have been truly privileged to work with him.

I would like to thank Professors P.J. Hirshfeld, J.M. Graybeal, D.H. Reitze, and J.R. Reynolds for reading this dissertation and for their interest in serving on my supervisory committee.

Thanks also go to all my past and present colleagues in Tanner's group for their friendship, useful conversation and cooperation throughout my graduate work, M.A. Quijada, Y.-D. Yoon, A. Zibold, J.L. Musfeldt, K. Kamaris, U. Akito, A. Memon, C.D. Porter, L. Tache, D. Stark, D. John, J. Laveigne, V. Boychev, and S.-K. Hong.

I would like to acknowledge those who have generously supplied high-quality samples which were essential to the completion of this dissertation. They are Drs. M.Y. Li and M.K. Wu (Tsiang Hua University, Taiwan), M.J. Burns and K.A. Delin (California Institute of Technology) for studies of YBa2Cu307_8 films, Beom-Hoan 0 and J.T. Markert (University of Texas), G. Cao and J.E. Crow (National High Magnetic Field Laboratory) for studies YBa2Cu3O7-6-family single crystals, R.J. Kelly and M. Onellion (University of Wisconsin), H. Berger, G. Margaritondo, and L. Forr6 (Ecole


ii










Polytechnique F6d6rale de Lausanne, Switzeland) for studies of Bi2Sr2CaCu208family single crystals, A.E. Pullen and J.R. Reynolds, L.-K. Chou and D.R. Talham (Department of Chemistry, University of Florida) for studies of organic conductors.

In addition, I have greatly appreciated assistance from Dr. Y.J. Wang at the National High Magnetic Field Laboratory. I am also in the debt of Professor M.W. Meisel, Dr. J.S. Kim and T. Steve for the ac susceptibility measurements of organic conductors and high-Tc materials. I would like to thank Dr. K.A. Abboud for X-ray experiments of organic conductors. I thank the technical staff members in the physics department machine shop, electronic shop, and cryogenic for their efforts.

I would also like to take this opportunity to thank my parents for their love and support. Finally, but most importantly, very special and sincere thanks go to my wife Yu-Huei Chu, whose constant love, dedication, encouragement and guidance led me to the path and helped me to stay there.

Financial support from the NSF (Grant No. DMR-9403894) is gratefully acknowledged.


iii















TABLE OF CONTENTS


ACKNOWLEDGMENTS .....................................

ABSTRACT.............................................


. . ii .. 11


CHAPTERS


I. INTRODUCTION .................................

II. FAR-INFRARED PROPERTIES OF SUPERCONDUCTING
YBa2Cu307_6 FILMS IN ZERO AND HIGH MAGNETIC FIELDS


. . . .. .....1



........................ .. .. 3


Introduction ...........
Experimental ..........
Results ..............
Zero-field spectra ...... Magnetic field studies ... Discussion ............
Dielectric function models The vortex dynamics ... Summary .............


.3
.6
.9
.9
10
12 12 16
21


III. DOPING-INDUCED CHANGE OF OPTICAL PROPERTIES IN
UNDERDOPED CUPRATE SUPERCONDUCTORS .........


..... 37


Introduction ............
Experiment ............
Sample characteristics . .. Optical measurements . ... Results ...............
Room-temperature spectra.


37 39 39
40 41 41


iv


-. . . . . . . . ..-.-- - . . . . . . . . . . . . .
. . . . . ... - - - - - - - - - . . . . . . . . . . .
-. . . . . . . . ..-.-- - . . . . . . . . . . . . .
. ... . . .. . - - . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . .










Temperature dependence in the infrared ...................... 43
D iscussion . ..... ...... ..... ..... ..... ..... .......... 44
Low-frequency spectral functions . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Dielectric function models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Quasiparticle scattering rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
Superconducting response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Sum m ary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61


IV. OPTICAL STUDY OF UNTWINNED (Bii.57Pbo.43)Sr2CaCu2O8+6
SINGLE CRYSTAL: AB-PLANE ANISOTROPY .................. 84


Introduction ............................................ 84
Experimental ........................................... 86
Results and Discussion ..................................... 89
Polarized reflectance .................................. 89
Optical conductivity ..................................... 90
Oscillator strength sum rule ............................. 92
Dielectric function models ................................. 93
Superconducting state ................................. 98
Sum m ary .......................................... 103


V. AB-PLANE OPTICAL SPECTRA OF IODINE-INTERCALATED
Bii.9Pbo.1Sr2CaCu2O8+b: NORMAL AND SUPERCONDUCTING
PROPERTIES ...................................... 113


Introduction ........................................... 113
Experim ental ...................................... . 115
Results and Discussion .................................... 116
Reflectance spectrum ................................... 116
Optical conductivity .................................... 117
Oscillator strength sum rule ............................ 120
Quasiparticle scattering rate ............................. 122
Spectral weight in the condensate ........................ 126
Sum m ary. .......................................... 127


VI. AB-PLANE OPTICAL PROPERTIES OF NI-DOPED Bi2Sr2CaCu208+6 137


v










Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
Experimental Techniques and Data Analysis .................. 138
Comparison of Ni-Doped to Pure Bi2Sr2CaCu208+6 . - . . . . . . . . . . 140
Temperature Dependence of Ni-Doped ...................... 141
Reflectance spectrum ................................... 141
Conductivity and dielectric function ...................... 142
Two-component model .................................. 143
One-component analysis ................................. 147
Spectral weight .................................... 149
Superconducting-state properties .......................... 150
Sum m ary .......................................... 152

VIII. CONCLUSIONS ..................................... 165

APPENDICES

A STRUCTURE AND PHYSICAL PROPERTIES OF
A NEW 1:1 CATION-RADICAL SALT, (-(BEDT-TTF)PF6 ........ 169

B OPTICAL AND TRANSPORT STUDIED OF Ni(dmit)2
BASED ORGANIC CONDUCTORS ........................ 213

REFERENCES .............................................. 249

BIOGRAPHICAL SKETCH . ................................. 268


vi















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy



EFFECTS OF HIGH MAGNETIC FIELD AND
SUBSTITUTIONAL DOPING ON OPTICAL
PROPERTIES OF CUPRATES SUPERCONDUCTORS By

Hsiang-Lin Liu

August 1997


Chairman: David B. Tanner
Major Department: Physics

Infrared and optical spectroscopies have been applied to study both the normal state and superconducting state electronic properties of cuprate superconductors. Two important parameters used in our experiments are the applied magnetic field and substitutional doping.

Varying the magnetic field at constant temperature allows us to study the vortex dynamics in the high-temperature superconductors. In contrast to several previous reports, we do not see any field-sensitive features in either far-infrared reflectance or transmittance spectra of YBa2Cu307.. thin films at low temperatures. Only at fields and temperatures where the dc resistance is not zero-on account of dissipative flux motion-there is a field-induced effect in far-infrared transmittance.

We studied the ab-plane optical response of Y-doped Bi2Sr2CaCu208 and Prdoped YBa2Cu307-6 single crystals from underdoped to optimally doped regimes. It


vii










is difficult to relate our results of low-frequency spectral functions to the normal-state pseudogap. We have also found that there is a "universal correlation" between the numbers of carriers and the transition temperature. This correlation holds whether one considers the number of carriers in the superfluid or the total number of carriers.

The polarized spectra of Pb-doped Bi2Sr2CaCu208+6 were also investigated. We find that although Pb doping removes the b-axis superlattice structure, there is a definite ab-plane anisotropy of optical properties above and below T,. Our results provide evidence that within the CuO2 plane the electronic structures of these Bibased cuprate superconductors are anisotropic, irrespective of the superstructure in the Bi-O layer.

In the iodine-intercalated Bi2Sr2CaCu208+6 sample, we find that the infrared phonon spectrum and the visible-ultraviolet interband transitions are modified after intercalation. The ab-plane optical conductivity results support the idea that intercalated iodine increases the hole concentration in the CuO2 planes. The iodine is present as ions, most likely as I3

Finally, the ab-plane optical spectra of Ni-doped Bi2Sr2CaCu208+6 were measured. We suggest that the low-frequency feature in the normal-state o-1 (w) is associated with the significant disorder induced by Ni impurities. In the superconducting state, a smaller superfluid density than implied by T, from the Uemura line could be connected with the effect of impurity-induced disorder.


viii














CHAPTER I
INTRODUCTION


Eleven years have passed since the first cuprate superconductor was discovered.1 Although we have not yet reached a final goal of the elucidation of the high-T, mechanism, a tremendous number of experimental techniques and theoretical work have revealed its electronic properties. Infrared and optical spectroscopies have played an important role in clarifying the electronic state of cuprate superconductors.2A Infrared light probes the dynamics of the free carriers, the nature of charge-transfer and other low-energy excitations, the superconducting gap (in principle), phonons, and other aspects of the electronic structure. Because infrared penetrates a substantial distance (- 0.2-1 pim) into the material, it is less sensitive than other probes (tunneling and photoemission, for example) to surface damage, especially if the surface layers are nonconducting.

This dissertation is organized in such a way that each chapter is essentially selfcomplete and can be read without assuming special knowledge from another chapter. We present an experimental study of the infrared properties of high-Tc superconductors. The reflectance and/or transmittance of these materials has been measured at temperatures between 4.2 K and 300 K over wavelengths from the far-infrared (35 cm-1 or 4.5 meV) to the near ultraviolet (40000 cm-1 or 5 eV). Furthermore, two important parameters used in our measurements are the applied magnetic field and substitutional doping. From these experiments the optical conductivity, 0-1(w), dielectric function, f1(w), and other optical properties can be estimated.

When a magnetic field is applied to the high-Tc superconductors, their mixed state properties are characterized by the existence of vortices. There has been con-


1







2


siderable interest in vortex dynamics in the high-T, materials, including their ac properties. In our work, we report the far-infrared reflectance and transmittance measurements of YBa2Cu307_b films. We use reflectance and transmittance to extract frequency-dependent optical conductivity as a function of temperature and applied magnetic field. Our discussion will concentrate on the relationship between the spectrum changes in a magnetic field and the two distinct parts (vortex solid and vortex liquid states) of the magnetic phase diagram.

Change of properties with varying carrier density is also of central concern for the experiments and theories aiming to understand the high-Te mechanism. We have examined the optical properties of Y-doped Bi2Sr2CaCu208 and Pr-doped YBa2Cu307_6 single crystals from under- to optimally-doped regimes. We will address several interesting issues. Among them are the following: Is there a pseudogap in the normal state? What are the nature of the low-lying electronic states? What governs the lifetime of the charge carriers? Does the low-frequency spectral weight evolve with doping?

In order to provide further information on the nature of the ab-plane anisotropy, the role of interlayer coupling, and localization effects in the charge transport, we have investigated the optical properties of several Bi2Sr2CaCu2O8-family materials. We chose Pb-doped Bi2Sr2CaCu208+6 samples because Pb doping changes the periodicity of the superstructure along the b axis. By performing the polarized reflectance measurements, we will show that there is definite ab-plane anisotropy above and below T,. The effect of iodine intercalation is to increase interlayer coupling. We will discuss the change of ab-plane optical properties after intercalation and the valence state of intercalated iodine atoms. Ni is a dopant, which substitutes for the Cu atoms in the CuO2 planes. We will study the influence of impurity-induced disorder on the ab-plane optical properties in the Ni-doped Bi2Sr2CaCu208+.














CHAPTER II
FAR-INFRARED PROPERTIES OF
SUPERCONDUCTING YBa2Cu307.-6 FILMS IN ZERO AND HIGH MAGNETIC FIELDS



Introduction

The electronic properties of high-Te superconductors are affected by the application of magnetic fields. The simple picture of the high-Tc materials, in the mixed state, is the sample penetrated by an array of magnetic vortices each of which contains a quantized amount of magnetic flux. In the applied current density fext and the average magnetic flux density B, there will be a Lorentz force density f = Je x B on the vortices. If the vortices are at rest, the resistance will be effectively zero. If the vortices are moving with a mean velocity V, an electric field . = 6 x B appears and there is finite resistance. However, the behavior of the complex dynamics of vortex motions in the presence of viscous, pinning forces, and fluctuations either of thermal origin or due to the influence of defects in the sample becomes complicated and is not yet well understood. Indeed there have been controversies regarding the ac properties of the vortices in the high-T, superconductors.

In spite of the challenges, there is growing interest in vortex state electrodynamics on the high-Tc superconductors over a broad range of frequencies.57 Historically, microwave experiments have been widely used to study the vortex dynamics in type II superconductors.8 When the vortices are pinned, their dynamics are invisible to dc transport. On the other hand, microwave measurements can sense the fluctuations about the pinning sites. Measuring the complex surface impedance provides information related to the effective pinning force constant and vortex viscosity. There were


3







4


already numerous measurements on the effect of magnetic field on the microwave response functions of the high-Tc superconductors.-12 It is generally agreed that the microwave results are affected by two mechanisms: vortex motion and superconducting condensate depletion. More recently, terahertz time domain spectroscopy spans the frequency from 100 to 1000 GHz (3.3-33.3 cm1).13-5 The nonlinear dependence of the complex conductivity as a function of magnetic field has been interpreted in terms of enhanced pair breaking due to nodes in the gap function. At higher frequencies, far-infrared spectroscopy has been applied to investigate the vortex dynamics in the high-T, superconductors.13-15

During the past several years, the far-infrared properties of the high-Te superconductors in zero magnetic field have been extensively studied in an effort to understand the mechanism of high-temperature superconductivity.4 More recent interest has concentrated on the change in the far-infrared response in an applied magnetic field. In most cases, evidence for additional absorption is seen. Still, there are some contradictions among these measurements. The early report by Brunel et al.16 on the reflectance -4 measurements of Bi2Sr2CaCu208 (BSCCO) at several far-infrared frequencies w as a function of temperature T and magnetic field H up to 17 Tesla, has inferred a value for the superconducting gap by setting 2A(T,H) = hw at the T and H where -4 first drops below the low-T, zero-H value. In their data, the drop in farinfrared reflectance corresponds to the onset of the resistive state and thus only occurs at the higher temperatures or fields. In contrast, the far-infrared transmittance measurements through a thin film of YBa2Cu307-6 (YBCO) in a strong magnetic field by Karrai et al.17,18 show an increase in transmission below - 125 cm-1 with increasing field. This is attributed to the dipole transitions associated with bound states in the vortex cores. Evidence for magneto-optical activity was also found, interpreted as cyclotron resonance in the mixed state. These effects occurred at temperature as low







5


as 2.2 K and in magnetic fields up to 15 Tesla. Later, several theoretical calculations of the optical response of the vortex core states have been published.1-22 The theory of Hsu including the vortex motion21'22 describes the experimentally chiral response'8 very well, but the agreement for the nonchiral response at ~ 65 cm-1,17 which the authors attributed to the vortex core resonance, is only partial. Shimamoto et al.23 observed the general trend of far-infrared transmission to increase on both YBCO and Bi2Sr2Ca2Cu30, films with fields to 100 Tesla. The field-induced transmission change abruptly increases at around T, with decreasing temperature and tends to saturate to a constant at temperature down to 10 K. The authors explained this feature by a flux low model. Gerrits et al.24 reported practically no influence of the magnetic field up to 15.5 Tesla on the far-infrared reflectance measurements of YBCO thin films at 1.2 K. Eldridge et al.25 measured the ratio of normal incidence reflectance -4 of a YBCO film in a magnetic field to that in no field, in conjunction with a separate measurement of R(0), to obtain the absolute values of R(H= 0.7, 1.4, and 3.5 Tesla) at 4.2 K. A Kramers-Kronig analysis then gave the field-dependent conductivity which shows a broad resonance between 50 and 250 cm-1. They are able to fit the shapes, but not the magnitude, of the peak by the theory involving vortex motion with pinning.

In this chapter, we report the far-infrared reflectance (M) and transmittance (.1) measurements of YBCO films at temperatures between 4.2 and 300 K and in magnetic fields up to 30 Tesla. This work is different from earlier spectroscopic studies, as we use M and 3 to extract frequency-dependent optical conductivity as a function of temperature and applied magnetic field. Comparison of temperature-dependent results with previous published data26,27 achieves a consistent description of the twocomponent dielectric response, with the free carrier component condensing to form the superfluid below T. However, as varying the magnetic field (with H perpendicular to







6


the ab plane and with unpolarized light) at constant temperature as low as 4.2 K, the conductivity spectrum shows no discernible field dependence. This observation differs from several previous far-infrared measurements in this temperature range. Only at fields and temperatures where the dc resistance is not zero-on account of dissipative flux motion-is there a field-induced effect in infrared transmittance.


Experimental

We have studied three types of YBCO films. Type one of samples was made by a KrF excimer laser (wavelength of 248 nm) on YAlO3 substrates at Jet Propulsion Laboratory. The YAlO3 substrates were 0.25-mm-thick, (001)-oriented and doped with 20% Nd on Y sites to suppress twinning. The nominal growth process is done in the following way. The substrates are mounted on Haynes alloy plates using Ag paint. These are transferred into the deposition system via a load-lock. Those substrates are buffered using a 200A PrBa2Cu307_6 (PBCO) layer deposited by pulsed laser deposition at 790*C, 400 mTorr of 02, at a fluence of 1.6 J/cm2. Substrates are heated radiatively and monitored by a thermocouple that is cross-checked by an optical pyrometer prior to film growth. The PBCO layer is followed by a YBCO layer deposited at 810'C, 200 mTorr of 02, and 1.6 J/cm2. The deposited bilayer is cooled in situ at 40*/minute in a 500-650 Torr 02 atmosphere from the growth temperature down to room temperature. The film thickness is typically d = 300 ~ 500A. The second type of samples was also prepared by pulsed-laser ablation at Tsing Hua University. The films (d = 400 - 600A) were grown on 0.5-mm-thick, (001)-oriented MgO substrates. The laser energy for YBCO target is about 1.5 J/cm2. During the deposition, the oxygen pressure and substrate temperature are 400 mTorr and 730*C, respectively. The film is cooled in situ in one atmosphere 02 to ~ 500* over an hour period, and then followed by slow-cooling to room temperature. The third sample is 5000-A-thick film deposited on a SrTiO3 substrate by the similar method.







7


All the samples have been structurally characterized by x-ray diffraction, which has clearly shown their c-axis orientation. The superconducting properties of films have been determined by dc resistivity or ac susceptibility measurements. The characteristics of all samples are listed in Table 1. Figure 1 illustrates the temperaturedependent dc resistivity data. The 5000-A-thick film gives a slight higher onset temperature and sharper transition width. On the other hand, samples prepared in similar conditions have shown close values of resistivity at room temperature.


Table 1. Sample characteristics.

Sample T, A T, Odc(at 300 K)

K K Q-1cm-1

300A YBCO/200A PBCO/YAlO3 83.5 3.5 1820

5ooA YBCO/200A PBCO/YAlO3 85.0 2.5 1700

400A YBCO/MgO 83.0 3.0 2500

600A YBCO/MgO 86.7 2.8 2800

50ooA YBCO/SrTiO3 88.0 0.5 3100



All thin films have been studied in reflectance (9) and transmittance (5), whereas the 5000-A-thick film on SrTiO3 has been studied by -4. Temperaturedependent (10-300 K) - and 7 at zero magnetic field were performed from 35 to 600 cm-1 using a Bruker 113V Fourier transform spectrometer equipped with a constant flow helium cryostat. Far-infrared studies in a magnetic field have been carried at the National High Magnetic Field Laboratory. Our measurements used a Bruker spectrometer and light-pipe optics to carry the far-infrared radiation through the magnet. The sample probes in conjunction with a 20-Tesla superconducting magnet are designed to enable alternate sample and reference measurements (for both -4 and







8


.7), eliminating instabilities of the spectrometer. For the reflectance data, an Au mirror has been used as a reference, while the transmittance was done relative to an empty diaphragm. The absolute values of the overall -4 and .5 in the sample are obtained at 4.2 K and applied fields up to 17.5 Tesla. We also employed a 30-Tesla resistive magnet to study the magnetic field effects. Note that in this configuration, only the transmittance ratio is accessible. Thus, we report [.(H) / T(0)] at the constant temperature running over a range between 4.2 and 100 K. In all measurements, the unpolarized far-infrared radiation was incident nearly normal to the film, so that the electric field was in the ab plane. The magnetic field H was perpendicular to the ab plane. A detailed description of the experimental setup is given elsewhere.28

The complex dielectric function e(w) or optical conductivity a(w), [e(w) = 1 +
] was directly calculated from the measured -4 and .7 in the far-infrared region. To deal with dispersive and absorption effects in the substrate, the reflectance Rsub and transmittance Jsub of a bare YAlO3 and MgO were also measured at each temperature and magnetic field where the film data were taken. The absorption coefficient a(L) and the index refraction n(w) of the substrate were then used in analysis of the data for the films. In this case, we found for the calculated dielectric response at low frequencies (w < 100 cm-1) is comparable to those obtained by optical reflectance of bulk, single crystal, and thick-film samples followed by Kramers-Kronig analysis where extrapolation to zero and infinite frequencies were needed. A detailed discussion of the analysis for transmittance and reflectance data has been given in previous work.26,27







9
Results
Zero-field spectra

The zero-field far-infrared reflectance and transmittance of 500A YBCO/200A PBCO/YAlO3 and 400A YBCO/MgO films at six temperatures below and above T, are shown in Fig. 2. Measurements on 300A YBCO/200A PBCO/YAO3 and 600A YBCO/MgO films revealed similar results. We have found small transmitted intensity (37 < 15%) for different films, where generally much of the behavior over 100-600 cm-1 is due to phonon processes in the YAlO3 and MgO substrates. Despite the fact that the far-infrared spectra are complicated by the substrates, one can clearly observe the intrinsic response of the YBCO films in the data. Below Tc, superconducting films strongly screen the applied electromagnetic field giving the low-frequency reflectance close to unity, while the transmittance tends to zero. A finite transmittance at w = 0 corresponds to a finite dc conductivity. Our zero-field spectrum of a 400A YBCO/MgO film is compatible with that on a 480A YBCO/MgO film reported previously by Gao et al.26'27

We extracted the real and imaginary parts of the conductivity directly from the experimental reflectance and transmittance of the films. In the following, we concentrate the behavior on the far-infrared region below 150 cm-1 for the YBCO film on the YAlO3 substrate and 300 cm-1 for the YBCO film on the MgO substrate since both substrates are mainly opaque above these frequencies at all temperatures.29 The upper panels of Fig. 3 (a)-(b) show the real part of the conductivity a1(w). In the normal state, al(w) approaches the ordinary dc conductivity. In the superconducting state, the spectral weight loss can be seen for T < 80 K, implying a shift of weight to the origin. Focusing on the data below 100 cm-1, we observe that a, initially increases with decreasing temperature, reaching a maximum at around 75 K, an then falls again at lower temperature. In contrast, this feature is flattened out at higher frequencies. We will bring further evidence of this point later when dealing with







10


the model analysis of the data. At T < Tc, if extrapolated 01 to zero frequency, 01 (W -* 0) reaches a value of about 6000 cm-1. This is approximately two times larger than the Kramers-Kronig results seen in the a-axis conductivity of YBCO single crystals,30,31 but coincides with those previous data by microwave techniques.32

The imaginary part a2(w) is plotted in the lower panels of Fig. 3 (a)-(b). When T < Tc, U2(w) follows an 1/w dependence for w < 100 cm-1, consistent with the behavior of London electrodynamics. In contrast, o02(w) falls off more slowly than 11w at higher frequencies, on account of both the broad mid-infrared contribution and a remaining normal Drude component. We also notice that at low frequencies, 0.2(W) > 0.1(w), indicating the inductive current dominates over the conduction current in the superconducting state. When the temperature is increasing, 0-2(w) decreases monotonically and changes the slope at the superconducting transition. Above T, (T = 100 K), 0.2(w) extrapolates to the origin, as expected for a normal metal. To this end, it is important to point out that the optical conductivity o.(w) = (w/47r)Im[e(w)1] can be well fitted by the model discussed later. Magnetic field studies

In Fig. 4 we show the reflectance and transmittance of a 500A YBCO/200A PBCO/YAlO3 film taken at 4.2 K and at several magnetic fields. We observed practically no influence of the magnetic field on the infrared reflectance of the film. Moreover, the field-dependent features in the transmittance spectra are due to impurity effects in the YAlO3 substrate. The magnetic field and frequency-dependent conductivity of this film are shown in Fig. 5. The spectra show no discernible field dependence at 4.2 K. This observation differs from previous fax-infrared measurements in this temperature and frequency range.17,23,25 Despite the lack of field dependence in the either a, or 0.2 spectra, two interesting observations can be made. First, with the external field perpendicular to the ab plane of the superconducting YBCO film,







11


no far-infrared magnetoresistance was detected at 4.2 K and in the high-field regime. Second, down to the low-frequency limit (- 35 cm-1) of our measurements, the dielectric response does not change with magnetic field. Our results differ from the data obtained in the terahertz studies which reported the change in the 01 and o.2 on YBCO and BSCCO films over a broad range of field, frequency, and temperature.13-15

Figure 6 shows the temperature- and field-dependent reflectance spectra of the 5000-A-thick film. There it is shown in the upper panel of Fig. 6 that the low temperature reflectance is unity at w -- 0. Upon increasing frequency it falls off slowly, with a pronounced shoulder at - 450 cm-1. On the other hand, the lower panel of Fig. 6 displays the far-infrared reflectance of the film at 4.2 K as a function of magnetic field. We find no field-induced effects in the spectra. In particular, the field independence of the 450 cm-1 edge favors the non-superconducting explanations of this feature. It is generally accepted that this structure is due to interaction of an electron continuum with LO phonons along the c axis.33 Again, our results are in agreement with one earlier experiment,24 but in contrast to several previous reports.17,23,25

To investigate further, the magneto-transmission measurements taken at several temperatures and magnetic fields for both 400A and 600A YBCO/MgO films are shown in Fig. 7, 8 (a) - (d), respectively. The data were obtained by taking the ratio of the transmission of the sample at H to the zero-field transmission. It is clear that the ratio for the 400A film did not show any discernible field dependence at 4.2 and 50 K with fields to 27 Tesla. Similarly, we do not find any evidence for changes in the transmission ratio for the 600A film in this temperature and field range. Here it is necessary to point out that typical noise variations of our measurements in a magnetic field are on the order of 1%. On the other hand, we are unable to pursue our studies at lower frequency (w < 35 cm-1) on these films due to the low transmitted intensity (progressively deteriorating signal to noise ratio) in the superconducting state. When







12


the temperature is raised above 60 K, at 35 cm-1 the transmission of these films is seen to change by more than 5% with increasing fields from 6 to 27 Tesla, while the changes at higher frequencies (w > 100 cm-1) are not well resolved within our experimental error. It should be noted that the large magnetic field induced increase in transmission at low frequencies occurs at a temperature not too far below Tc. In contrast, the spectra change sign at 95 K for the 400A film, and there is a decrease of the transmission with applied field.

Discussion

Dielectric function models

In this section we turn to an analysis of the conductivity as obtained from the reflectance and transmittance data. We first consider the temperature-dependent spectra of the films in the normal state at zero field. There has been much discussion over the two-component and the one-component pictures to describe the optical conductivity of high-Te superconductors.4 Two-component model views the conductivity as two sets of charge carriers comprising of both a Drude contribution centered at w = 0 and a secondary mid-infrared absorption band arising from bound charges such as interband transitions. One-component model assumes a single carrier with a frequency dependent scattering rate due to coupling between the carriers and optically inactive excitation, such as spin excitations.

Because the data extend only to 150 cm-1 in the 500A YBCO/200A PBCO/YAlO3 film, we found that the Drude model can describe the optical conductivity well. In the case of the 400A YBCO/MgO film up to 300 cm-1, it seems necessary to allow for a second component in addition to the simple Drude one. The dielectric function is written as
2 2
WPD ope + 1
e(w) = - I + . + eir
W(W + i/.TD) L02 _ W2 _ W7







13


where the first term represents the Drude component described by a plasma frequency WpD and scattering rate 1/,rD; the second term is a Lorentz oscillator to represent one additional absorption band which is at frequency we, has oscillator strength wp,, and width -ye. The last term, ei,, is the high frequency limit of e(w), which includes higher frequency interband transitions.

In the superconducting state, a two-fluid analysis is used. Here, it is assumed that a fraction of the carriers (the thermally excited quasiparticles) display normal Drude behavior whereas the remaining part condenses to form a 6 function at w = 0. The dielectric function is expressed as

2 2 2
E _(__) _ . -. + .__ _ + (2)
w(w + 10+) w(w + /rD) We2 - W2 - We+, where wp, represents the oscillator strength of the superconducting condensate, iO+ is the scattering rate of the 6 function at T < T,. The quantity 2+w,2 = 2 gives the total numbers of carriers in the two-fluid model. A consistent and independent check of the fitting procedure is to compute the real and imaginary parts of the conductivity of the film with the parameters that we have obtained by fitting the experimental transmittance data. We then recall the reflectance data and their Kramers-Kronig form using the 0l and 0'2. It is found that the experimentally measured single bounce reflection of the substrate [R, ~ (-,)2 J agrees with the calculated reflectance spectra.

Figure 9 (a) shows the experimental (symbols) and fitted (solid lines) conductivity spectra of a 500A YBCO/200A PBCO/YAlO3 film at 20, 100, and 300 K. We fixed ei,. = 25 and varied the two-fluid parameter w, and wp, as well as the quasiparticle scattering rate 1/rD. It turns out that the models give reasonably good fits to the experimental data both in the normal and superconducting state. The Drude plasma frequency, wpD = 7100 100 cm-1, is essentially temperature independent.







14


We also found that the value of superconducting plasma frequency wps, obtained from the above analysis, is about 6000 100 cm-1 at 20 K. The superfluid density fraction [f,(20 K) = 2S(20 K)/wD is estimated to be 71%. The inset of Fig. 9

(a) displays the temperature-dependent scattering rate 1/rD from the free-carrier or Drude contributions. It appears that 1/rD has a linear temperature dependence for T > Te, whereas below T, the two-fluid model gave a rather sudden drop in 1/rD with saturation at T < 50 K. In the normal state, the linear 1/rD is a unique property of the copper-oxide superconductors and reflects the dc resistivity data. Writing h/rD = 27rAD kBT + hiro, AD is the dimensionless coupling constant that couples the charge carriers to the temperature-dependent excitations responsible for the scattering. In addition, the zero temperature value 1/ro is assumed to result from elastic scattering by impurities. We can obtain the coupling constant and intercept, from the straight line fit, as AD - 0.23 and 1/ro ~ 80 cm-1, As was stated previously, the temperature-dependent oi(T) at low frequencies exhibits a peak below T,. The physical origin of this behavior has been discussed previously.27,34,'5 The peak in 01 is attributed to the rapid drop in the quasiparticle scattering rate combined with a more slowly decreasing normal-fluid density.

In the case of the 400 A YBCO/MgO film, we found that we could obtain good fits by adding one more oscillator, we = 10000 cm-1, w, = 206 cm1 and Ye = 600 cm-1. Because the large lattice mismatch exists between the YBCO film and MgO substrate, defects or disorder in the interface layer might be responsible for this absorption band. Fitted conductivity spectra are shown in Fig. 9 (b). The parameters that fit the spectra are the Drude plasma frequency WpD = 8500 100 cm-1 and the superconducting plasma frequency cps = 7000 100 cm-1 at 10 K. The fraction of superfluid condensate is about 68% at T < T. Our results are similar to the previous work on the analysis of a 480A YBCO/MgO film by Gao et al.26,27 In addition, the







15


inset of Fig. 9 (b) shows the normal-state 1/rD is linear in temperature; it decreases quickly below Tc. 1/rD from the inelastic and elastic scattering processes gives the values of A - 0.20 and 1/ro ~ 66 cm-1, respectively. Taking the Fermi velocity to be VF = 1.4 x 107 cm/sec36 and using the scattering rate of 1/Dr(100 K) = 180 ~ 200 cm-1 for the above two films, we can estimate the mean free path (I = VFr) about 40 A. This evidence (I > , where the superconducting coherence length is about 10-15A in the cuprates) added to the small value of AD indeed suggest that our films are clean-limit and weak-coupling superconductors.

Concerning the superconducting fraction f,(T), this quantity is essentially a measure of the strength of the 6 function in o-1(w) and is related to the superconducting penetration depth AL. In Fig. 10 we plot the frequency-dependent penetration depth AL(w), defined as AL(W) = c2/47rwo2(w) where c is the light speed, for our YBCO films at T < T. The fact that AL(w) shows some frequency dependence below 150 cm-1 is an indication that not all of the free carriers have condensed into the 8 function. The penetration depth can be converted to the plasma frequency of the condensate, AL = c/wps. The extrapolated zero-frequency value AL(w -+ 0) is found to be 2600 100A and 2400 t 100 A for 500A YBCO/200A PBCO MgO and 400A YBCO/MgO; this gives wp, = 6000 t 200 cm-1 and 6600 200 cm-1, respectively. We note that the translation of the superfluid oscillator strength from AL(0) is close to the fitting value in the two-fluid model. Also, it is worth mentioning that the penetration depth for our films is larger than 1600 ~ 1800A reported by infrared reflectance measurements of bulk YBCO single crystals31 and thick YBCO films.37 Two possibilities for this discrepancy can be made. First, there is incomplete condensation in our films; the smaller superfluid density yields the larger penetration depth. Second, the experimental uncertainty in the film thickness would affect the absolute value of the penetration depth.







16


The vortex dynamics

In the presence of a magnetic field the electrodynamic response of type-II superconductors is affected by vortex dynamics. We first discuss the magneto-optics data at our lowest temperature at 4.2 K shown in Fig. 4, 5, 6, 7, 8. Surprisingly, our spectra do not show any change with applied field, which is in agreement with one early work,24 but in contrast to several previous reports.16172325 To acquire a better understanding, we consider the simple picture at T < Tc: The vortex can be driven either by an ac electric field or by superflow. Due to our high-frequency field oriented parallel to the ab plane, the vortices oscillate within their pinning potential.38 Demircan et al.39 have implied the natural motion of the vortices in superfluid is of cyclotron type, i.e., adiabatically follows the superconducting condensate. In this case we have nondissipative vortex flow. The area of the vortex cores is in the normal state and the outside of them is in the superconducting state. The fraction area of the cores is H/Hc2(T) and H,2 is upper critical field. The dielectric function of this system at low temperatures may be written as

W2H H A j2
E w() = [ 10] [ -- p + +f
w(o + iO+) H,2 w(w + i/r5) Hc2 w(w + i/rD) _2 _ zW-Y
(3)
Here, 1/7, is the damping constant inside the vortex. The entire change in the dielectric response will be attributed to the pair-breaking effect and the quasiparticle excitations inside the vortex cores. Indeed, the depletion of the superfluid condensate has been seen in YBCO and BSCCO films using terahertz impedance measurements.13-15 In their data, the field dependence of the observed magneto-resistance Ap(B) is consistent with the pair-breaking playing a significant part.

One could question why such an effect is absent in our study. To substantiate this point, again we start to view the two-fluid model, which describes the conductivity in the superconducting state as the sum of normal (na) and superfluid (n,) contributions,







17


i.e., a(w) = o,(w) + an(w), where o,(w) = - ne2/im*w and oe(w) = (n.e2/m*)S(w). S(w) is the frequency dependence of the quasiparticle conductivity and initially dominated by the term of 1/[(1/rD - iw)]. The change in a(w) due to a conversion of super to normal fluid is given by Ao(w) = w,2DA(nn/n)[S(w) - i/wi. Specifically, Aa(w) is maximum at zero frequency and decreases rapidly with frequency for wTD > 1. In our present work, the experiments are limited to w > 35 cm-1 and the quasiparticle scattering rate 1/rD of our films is smaller than 50 cm-1 for T < 50K at zero field, shown in the inset of Fig. 10. Moreover, the change in Aa(w) is expected to be not big for fields up to our maximum field of 30 Tesla when H,2 is greater than 100 Tesla. Thus, it is possible to say that any change of the spectra should be relatively small in our far-infrared frequency and high-field range. Further study at very far-infrared frequencies is clearly needed to probe the effect of field-induced pair-breaking.

Many studies have focused on the quasiparticle local density of states inside a vortex core.40-6 The physics of the vortex core for a type II superconductor is usually described by the Bardeen-Stephen model. This model is based on the dirty limit description (I < ), which the motion of the quasiparticles gets well randomized within the core. The first calculations of the electronic vortex structure in the clean limit (I > ) and for H < Hc2 were performed by Caroli et al.40,41 Subsequently, Kramer and Pesch43" discussed the spatial structure of a vortex in a type-II superconductor in the clean limit and for s-wave symmetry of the order parameter. They showed the radius of a vortex core decreases proportionally to T with decreasing temperature. An important point underlying this peculiar behavior, namely the change of the core size as temperature is lowered, is the existence of a quasicontinuum of the bound states in the vortex core. In the quasiclassical limit we have kF > 1 and the energy of the lowest bound state (minigap) A2/EF OC 12 is very small. This picture is well established in the classical superconductors. However, for the high-T, super-







18


conductors the situation is quite different, since A is larger and EF is smaller than in the classical superconductors, ( 2 is by about four orders of magnitude smaller than in classical superconductors). Hence, only a few bound states in the vortex core are expected for the high-T, superconductors. Recent spectroscopic experiments appear to have confirmed this expectation.1747 A characteristic resonance has been observed by Karrai et al.17 in the mixed state of YBCO thin films at ~ 65 cm-1. They interpret their spectra as the vortex core resonance frequency. Based on the microscopic theory of vortex dynamic developed by Hsu,19,20 this feature corresponding core level spacing hMo = E1/2 - E-1/2 is about 40 cm-1 (~ 5 meV). Evidence for a large core spacing has also found in scanning tunneling spectroscopy (STS) on YBCO single crystals.47 In contrast, such dipole transition between the quasiparticle levels in the vortex core is not present in our high-field measurements.

In view of these differences, we suggest that anisotropic pairing (or gap) effect in the high-temperature superconductors might lead to the complexity of excitations inside a vortex core. We note that for the case of d-wave superconductors the quasiparticle levels in the vortex core have a number of significant differences from the s-wave case. In addition to the set of localized levels similar to that found in s-wave superconductors there are also continuum levels outside the core that are associated with s-wave admixture induced by the vortex.4850 Kopnin and Volovik"l pointed out in a clean d-wave superconductor, the electronic density of states induced by a vortex actually exhibits a divergency at low energies: Nvortex(E) ~ 1/IEI. It is a result of gap nodes in the excitation spectrum outside the vortex core. 1/E divergence will presumably be cut off in a dirty d-wave case. At a higher field, the distance between the cores becomes small; the electronic structure of the vortex core must be influenced by the competition between electrodynamic effects and spatial variations of the superconducting order parameter near the vortex core. Thus, it seems likely







19


that the excitations from the continuum levels might obscure the contribution of the E+1/2 state. Another possibility is that the oscillator strength of the E+1/2 state was too small to be seen in our present data. Furthermore, the STS experiments demonstrated very few quasiparticle states can exist inside an YBCO vortex core and vortex cores are in an extreme quantum limit.47 For our YBCO films, we may approach already this quantum limit, where the core region of the vortex is empty of the low-energy excitations. As is described previously, for frequencies below 200 cm-1, Karrai et al.18 also reported the chiral resonance on thin films of YBCO which the system exhibits free hole-like optical activity. Recently, several new chiral effects have been observed: the vortex pinning resonance,52 grain-boundary-induced vortex core excitations,53 and hybridization of the cyclotron and vortex core resonances with the pinning resonance.54 The chiral response will be a subject for further investigation in our future work.

We will now discuss the high-temperature magneto-transmission data. As can be seen in Fig. 7, 8 (a)-(d), the contrast between the high and low temperature data is striking. Above 60 K where the system enters the flux flow regime, we observed the field-induced increase in transmission at low frequencies. We note that at these elevated temperatures one may expect that vortices become more mobile and thermally activated (Brownian) motion becomes possible. The electromagnetic interaction of the induced currents with the vortex lattice due to the Lorentz force was treated explicitly in the early work of Bardeen and Stephen,42 and more recently by Brandt,55 Coffey and Clem,56 and Tachiki et al.57 In these models, the interaction with the vortices is treated phenomenologically by introducing an effective pinning force constant np, vortex viscosity 77, and vortex mass M. Therefore, the dielectric function which includes the contribution from the vortex motion is given by







20


W2 H Tv /rD 2 Pn pe
e ~ P = -[+ ] -+ . + fir
W2 Hc2 (1 - iwr, - Mw2/np) w(w + i/TD) L,2 _ L2 - jr
(4)

where r,, = 7/ icp is the relaxation time of the vortex motion. Unfortunately, it is difficult to relate our experimental data to the above model because the case of a clean limit in our films must be distinguished from the Bardeen-Stephen42 model which is valid in the dirty limit. Furthermore, we are presently unaware of any calculations for the vortex dynamics in the flux flow regime taking into account the influence of a clean limit and possibly anisotropic symmetry of the order parameter.

A feeling for an enhancement of the transmission with magnetic field may also be obtained in the following way. The total transmittance through a thin film of thickness d < A is dominated by the complex conductivity o = o+ + iW2. The transmittance is 58 . = 4n/[(yi + n + 1)2 + y22] where y1 + iy2 = (4ir/c)d(al + io2) is the film admittance. At temperatures where the dc resistance is not zero-on account of dissipative flux motion-the London screening and the imaginary part of the conductivity 02 is significantly reduced. Then, the transmittance is increased at low frequencies. In contrast, the transmittance above T, decreases, as would occur if al is increased. The cyclotron motion of normal carriers or excited quasiparticles might be the main mechanism of this normal-state magneto-absorption. Finally, we can map out the magnetic phase diagram for YBCO films from magneto-optics measurements and compare with the data from dc transport and I-V measurements.59,60 This comparison is shown in Fig. 11. As discussed elsewhere,61 the magnetic phase diagram for the high-Tc superconductors is not a quite simple case as shown in Fig. 11, and we cannot expect to be able simply to use far-infrared measurements to study the detailed character of the phase boundary on the H-T diagram. What is important is the ideas involved. To see that, at least in principle, there is relationship between far-infrared properties in a magnetic field and two distinct parts (vortex solid and







21


vortex liquid states) on the H-T phase diagram. At low temperatures the vortices are not easily moved due to pinning effects, i.e., vortex lattice is most likely a solid and the magnetic field has no effect on the spectra. However, when temperature is increased into the vortex liquid state and the flux pinning is overcome, vortex motion is driven by optical current and there is a corresponding change in the far-infrared properties. Thus, a magnetic-field-induced enhancement of the transmittance can be explained as a flux-flow phenomenon.

Summary

In summary, we have presented the temperature and magnetic field dependence of the far-infrared optical data on YBCO films where both the reflectance and transmittance have been measured. At zero field, we emphasized the two-component picture analysis for both the normal and superconducting states. The Drude plasma frequency is essentially temperature independent, whereas the scattering rate has linear temperature dependence in the normal state followed by a fast drop below T,. A weak-coupling strength AD ~ 0.20-0.23 is derived. The superconducting condensate carries most (~ 70%) of the free-carrier oscillator strength, evidence for the clean-limit in our films.

Varying the magnetic field at constant temperature allows us to study the vortex dynamics in the high-temperature superconductors. In contrast to several previous reports, we do not see any field-sensitive features in either far-infrared reflectance or transmittance spectra of YBCO films at temperature as low as 4.2 K. This observation suggests the following points: (1) The pair-breaking effects could be too small to be seen in our frequency and field range. (2) The anisotropic pairing (or gap) effects in the high-temperature superconductors might lead to the complexity of excitations inside a vortex core. The contrast between the high and low temperature data is striking. At a temperature not too far below their transition temperature, we observed







22


the field-induced increase in transmission at low frequencies, which can be explained as a flux flow resistance. It is unclear why this effect changes sign above T, and shows a decrease of transmission with applied field.

Though there are still a lot of controversies on the experimental data and even more on their interpretations about the far-infrared optical studies regarding the vortex dynamics, we hope that our preliminary results will stimulate more completely and rigorously experimental and theoretical work for understanding the electrodynamics of cuprates in a magnetic field.








23


YBa2Cu3076 films
300A YBCO/200A PBCO/YAIO3
- __ ___ 500A YBCO/200A PBCO/YAIO3
400A YBCO/MgO 600A YBCO/MgO
5000A YBCO/SrTIO,


50


K-


100 150 200 Temperature (K)


250


300


Fig. 1 The dc resistivity in the ab plane, as a function of temperature, for all
the YBCO films.


1.0


0.8


0.6 -


U

E


0.4K


0.2


0.0


I I I I I I I


0


i 1 - ' ' i ' ' ' ' i '








24


Photon Energy (meV) 20 40


60


20 K


50 K 75 K 100 K 200 K 300 K


I I I I I I I


(a) 500A YBCO/200A
20 K 50 K
- _ 75 K
__ 1 100 K
-- -200 K .. 300 K


PBCO/YAIO3 -


100


200 300 400 Frequency (cm 1)


500


600


Fig. 2 The measured far-infrared reflectance (upper) and transmittance
(lower) of (a) a 500A YBCO/200A PBCO/YAlO3 and (b) a 400A
YBCO/MgO films at six temperatures and at zero field.


0


1.0


0.8 0.6


0.4


Q)
0


.4
Q) GUf


0.2


0.0


0.20 0.15 0.10


a,

-

E V)


0.05


0.00


I


0


_ ,- . I ' I I


i


-


I








25


Photon Energy (meV)
0 20 40 60
1.0



0.8


U
C 0.6


Q.) 10 K
S0.4 - 50 K
Q_ .70 K
ry - - - 100 K

0.2 200 K
300 K


0.0



0.20 (b) 400A YBCO/MgO
)__ __ 10 K
c 50 K
o 0.15 - .70 K
+- _ __.. 100 K
E4-- _____ 20OOK
200 K
) ........ 300 K
0.10 -


0.05



0.00
0 100 200 300 400 500 600
Frequency (cm1)


Fig. 2-continued








26


Photon Energy (meV)
0 10 0 10 0 10 0 10 0 10 0 10


(a) F
20 K 50 K 75 K 100 K 200 K 300 K












20 K 50 K 75 K 100 K 200 K 300 K







-- - -- -


0 50 100 0 50 100 0 50 100 0 50 100 0 50 100
Frequency (cm~1)


0 50 100 150


Fig. 3 The real and imaginary parts of the optical conductivity extracted
from the experimental reflectance and transmittance of (a) a 500A YBCO/200A PBCO/YAlO3 and (b) a 400A YBCO/MgO films. The
symbols show the dc values.


E


E

C4

b


10000 8000 6000

4000 2000

0
25000


20000 15000 10000


5000


0







27


Photon Energy
0 20 0 20 0 20


(meV)
0


20 0 20


10000


0 100 200


0 100 200 0 100 200 0 100 200
Frequency (cm-)


0 100 200 300


Fig. 3-continued


E
7


E


8000 6000

4000 2000

0
25000


20000 15000 10000


5000


0


(b)
10 K _50 K 70 K 100 K 150 K













10 K 50 K 70 K 100 K 150 K






- f-- i - ---









28


Photon Energy (meV) 10 20


30


S____ 0 Tesla ~ _ 3 Tesla
-__--___ 6 Tesla
12 Tesla
- -- - -- 17.5 Tesla


500A YBCO/2OOA T = 4.2 K


0 Tesla 6 Tesla 12 Tesla 17.5 Tesla


^r


50


100 150
Frequency


200 (cm1 )


250


300


Fig. 4 The 4.2-K reflectance (upper) and transmittance (lower) of a 500A
YBCO/200A PBCO/YAlO3 film at several magnetic fields.


0


1.05 0.95


0.85


Q)
C



r


0.75 0.65


0.10 K-


4

E
(n
C:.
0
L.


PBCO/YAIO3


0.05 H


0.00


0



' .


. I .


, I







29


Photon Energy (meV)
5 10


- 6000

E


C 4000




2000


0 Tesla 6 Tesla 12 Tesla 17.5 Tesia


500A YBCO/200$A T =4.2 K


PBCO/YAO3,


0 Tesla 6 Tesia
--- -- ..12 Tesla
17.5 Telsa


0 50 100 150
Frequency (cm )


Fig. 5 The magnetic field and frequency-dependent conductivity of a 500A
YBCO/200A PBCO/YAlO3 film at 4.2 K.


0


U Li Li Li


15


0



20000 15000 10000 5000


E






N
b


0


I


8000


- - ---








30


Photon Energy
0 10 20 30 40


1.05


1.00


0.95


(meV) 50


60 70


10 K 70 K
___ ___100 K


i i i I i ; i i i i i i ! i i ! I .


5000A YBCO/SrTiO T =4.2 K
- - 0 Tesla


3 Tesla 6 Tesla 12 Tesla 17 Tesla


100


200 300 400
Frequency (cm-)


500


600


Fig. 6 The measured zero-field reflectance (upper) of a 5000A YBCO/SrTiO3
film at 10, 70, and 100 K. (Lower) displays the reflectance spectra at 4.2
K as a function of magnetic field.


a,
U
0
4
U a,
a,


0.90



0.85


1.00


Q)
0


4
0y


0.95


0.90 0.85


0


- ' - -







31


Photon Energy (meV) 10 15 20 0 5


I I I T I I I I I I II I I I I
(a) T = 4.2 K
12 Tesla
18 Tesla
27 Tesla -


10 15 20


'I I ' ~ ~ I
(b) T = 50 K
18 Tesla
27 Tesla


0
1.5





1.0





0.5
0


50 100


150


(c) T 72 K
18 Tesla 27 Tesla


0


50 100


'I'


(d) T 95 K
18 27


150


200


Tesla Tesla


I I I I I I I I I


50 100


150


0 50
Frequency (cm~')


100


150


200


Fig. 7 The magneto-transmittance at several temperatures and magnetic fields
for a 400A YBCO/MgO film.


5


. I I. . I . I . I


1.5 1.0 0.5


L
0






-


-







32


Photon
0 5 10 15 20


Energy (meV)
0 5


10 15 20


I I I I I I I I I I I I I I . I I I .
(a) T = 4.2 K


6 Tesla 12 Tesla 27 Tesla


1.5 1.0 0.5


I . I I 6 K I I
(b) T = 6 0 K


. I ,


____ 6 Tesla
27 Tesla


50 100 150 0 50 100 150 20C

(c) T 70 K (d) T 80 K
6 Tesla 6 Tesla


I I
18 Tesla 12 Tesla


50 100


150


0 50
Frequency (cm 1)


100


150


200


Fig. 8 The magneto-transmittance at different temperatures and magnetic
fields for a 600A YBCO/MgO film.


-I


.1 . . . I


0
1.5






1.0


CD.


0.5


0


-


'








33


Photon Energy
5 10


(meV)
15


A


20 K 100 K 300 K
dc
Fit


(a) 500A YBCO/2OOA PBCO/YAIO,.


60C


400 200


10000






8000 E 6000
T
C


4000 2000






0


0


AAAAAAAAAAAA AA.


I.


I I I I - -


50
Frequency


100 (cml)


150


Fig. 9 The real part of the optical conductivity (in dots and symbols) of (a)
a 500A YBCO/200A PBCO/YAlO3 and (b) a 400A YBCO/MgO films.
The solid curves are fit to the data using a two-component model for the dielectric function. The square symbols on the vertical axes show the dc conductivity values. The inset shows the temperature dependence of
Drude scattering rate, 1/Dr, obtained from the fit.


0


E


0 100 200 300
Temperature (K)


-H


0


e -


-








34


Photon Energy (meV)


0


2500w


0


E
-a
a


-






0 100 200 300
Temperature (K)


10
-r-m,


20


A
U


30


(b) 400A YBCO/MgO


500 400 300 200 100


0


--


0 50 100 150
Frequency


200 (cm )


10 K 100 K 300 K dc
Fit


Fig. 9-continued


15000 12500 10000


E
T

C:


5000


250


300


, , . . . ,


7500








35


Photon Energy


5


10


(meV)
15


YBCO (T YBCO (T


YBa2Cu307_ f


500A
___ __ __ 400A


-C


I


50
Frequency


100 (cm-)


150


Fig. 10 The superconducting penetration depth of a 500A YBCO/200A
PBCO/YA1O3 film at 20 K and a 400A YBCO/MgO film at 10 K.


0


5000


4000 I-


3000 I-


I--,


2000 H


1000


0


0


f ilms


=20 K) =10 K)







36


30 I I '


25-


L quid


Vort x


al
e


Vortex Solid


-


Meissner State


20


40 60
Temperature (K)


\Norrr
Stat AKA


80


Fig. 11 Magnetic phase diagram for YBCO films. The solid and dashed
lines represent the H - T diagram obtained from dc transport and I V measurements.59,60 The dotted-dashed line represents the expected Meissner phase. The square and triangular symbols are the magnetooptics data for 400 and 600A YBCO films, respectively. The open symbols represent H and T values where the change in transmittance from the zero-field value was small or zero (less than 2 %) whereas the filled symbols represent H and T values where the change in transmittance with field
was large (greater than 5 %).


20


U) I-


15k-


C.) C)
0


5




0


0


100


0 0


10 --














CHAPTER III
DOPING-INDUCED CHANGE OF OPTICAL PROPERTIES
IN UNDERDOPED CUPRATE SUPERCONDUCTORS



Introduction

The subject of normal state properties in the underdoped high-Te superconductors has received a great deal of attention recently.62 This interest is exemplified by the socalled "normal-state pseudogap" phenomenon observed in several different experimental techniques. The nuclear magnetic resonance (NMR)61-66 and neutron-scattering measurements67,68 first suggest the opening of a gap in the spin excitation spectrum on normal-state underdoped YBa2Cu3OT-b (Y123) and YBa2Cu408 (Y124). Meanwhile, for these underdoped materials, the in-plane resistivity is linear only above temperature T*, which itself is well above T,.69-71 Furthermore, angle-resolved photoemission spectroscopy (ARPES) experiments72-74 on underdoped Bi2Sr2CaCu208 (Bi2212) indicated the presence of a gap in the charge excitation spectrum at certain locations on the Fermi surface at temperatures above Tc.

Indications of normal-state, gap-like anomalies in underdoped cuprates have also been observed in infrared optical measurements as well.75-80 The c-axis spectra of underdoped Y12375,76 and Y12477 have conductivity depression below 400 cm-1, interpreted as the result of the formation of a pseudogap. This spectral structure appears at a temperature scale which matches the spin susceptibility determined from the NMR measurements and has been discussed in the context of the spin gap. In contrast, a pseudogap is not evident in the optical conductivity measured in the CuO2 planes. Instead, there is structure in the 1/r(w, T) in the ab-plane, a depressed


37







38


scattering rate at low frequencies and at temperatures a little above TC.78- The shape of the normal-state and the superconducting-state 1/r(w, T) are very close.

There are several open questions about this normal-state pseudogap. First, the energy of the pseudogap-like structure does not change with doping. It is commonly observed at 400 cm-1 in the c-axis conductivity and around 700 cm-1 in the ab-plane scattering rate. Also, it is unclear why there is apparent factor of 2 between these two energy scales. Second, the doping independence of the energy is in strong contrast to the behavior of spin gap temperature, which decreases with doping. Third, in the normal state o-1(w) exhibits a much larger spectral weight at high frequencies than would be present from the generalized Drude form with a frequency-dependent lifetime.

In order to address the issues mentioned we have measured the ab-plane reflectance of single crystals of Y-doped Bi2212 and Pr-doped Y123 with changes in carrier densities at doping level ranging from heavily underdoped to nearly optimally doped. Optical investigations, extending over a broad frequency range and at various temperatures, offer an effective way to study the energy and temperature dependence of intrinsic parameters characterizing these materials. We first describe a number of properties: the reflectance spectrum, the optical conductivity, and the effective carrier density. We then discuss how they might account for the evolution of the ab-plane spectrum with doping. Next, we focus on the low-frequency conductivity and spectral weight of a strongly underdoped Bi2212 sample (T, = 35 K) in the whole temperature range. We investigate whether the normal-state pseudogap leads to a change of the charge excitation spectrum that can account for the observed dc resistivity. Of particular relevance in this connection, is the identification of the energy and temperature dependence of the quasiparticle damping. We derive the scattering rate from both the one-component and the two-component pictures. In







39


one-component analysis, our results have been treated within the framework of the generalized Drude model and the marginal Fermi liquid theory.81,82 Depending on the model, we compare the different features in the scattering rate deduced from the spectra. To the end, considering the superconducting response for all doping level studied, observation of a superconducting gap has been a hotly disputed issue. Even though we cannot say anything definite about the superconducting gap in all our spectra, the amount of conductivity that condenses into the 8 function at w = 0 is given less ambiguously from infrared measurements. Our discussion concentrates on the relation between the transition temperature and the number of carriers in the superfluid or the total number of carriers.



Experiment


Sample characteristics

The experiments described here have been done on Bi2212 and Y123 single crystals. In these systems, there are two ways to reduce the carrier concentration on the CuO2 planes, and, thus prepare underdoped samples. One is to substitute an element in the crystal structure by another one with higher valence state. In this case the substitution of Y3+ for Ca2+ has been found to be most efficient in Bi2212.83 Heavily underdoped Bi2212 samples with T, = 35 K (Pb 50%, Y 20%), 40 K (Y 35%) were measured. Another way is to remove oxygen from the pure samples. By annealing the crystals in argon, one slightly underdoped Bi2212 with T, = 85 K was obtained. Details of sample preparation axe reported elsewhere.84 In the Y123 system, we studied three fully oxygenated Yj-ZPr Ba2C3O7- single crystals. Substitution of Pr for the Y atom in Y123 changes only the hole content in the CuO2 planes, while the structure of the CuO chains remains unaffected.85 The Pr-doped samples have a T,







40


of 92, 75, and 40 K, respectively, for x = 0, 0.15, and 0.35. The crystals were grown by a method described elsewhere.86

The dc-resistivity measurements as a function of temperature on five samples are depicted in Fig. 12. The resistivities of Bi2212 and Y123, with a T, = 85, 92 K respectively, follow a linear curve over a wide temperature range. At 300 K, the increase of the resistivity with Y or Pr doping is apparently due to the reduction of the carrier concentration, although disorder introduced by the doping may also contribute to this increase. Interestingly, as in all doped samples, the overall resistivity still shows metallic-like behavior down to the transition temperature. However, there is a characteristic change of slope dp/dT at temperature T* marked by arrows. The values of T* increase with increasing Y and Pr doping. This feature is similar to the one observed in underdoped Y123 by oxygen removal71 and Sr-doped La2-..SrCuO4 (La214).87,88 Since it is unlikely that the number of carriers increase below T*, it appears that the temperature dependence of the normal-state resistivity p = (m/ne2)(1/r) must be attributed entirely to the scattering rate. Thus, a slop change in the resistivity blow T* indicates a change of carrier scattering at low temperatures. Optical measurements

The optical reflectance of all crystals has been measured for the radiation polarized parallel to the ab-plane over 80-40000 cm-1 (10 meV-5 eV). In the high frequency range (1000- 40000 cm-1) range we use a Perkin-Elmer 16U grating spectrometer while the far- and mid-infrared (80-4000 cm-1) regions were measured with a Bruker IFS 113v Fourier transform spectrometer. For the later frequencies, the temperature of the sample was varied between 300 and 20 K by using a continuous-flow cryostat with a calibrated Si-diode thermometer mounted nearby. Determination of the absolute value of the reflectance was done by coating the sample with a 2000A film of Al after measuring the uncoated sample. The spectra of the uncoated sample were then







41


divided by the obtained spectrum of the coated sample and corrected for the know reflectance of Al. The accuracy in the absolute reflectance is estimated to be 1%.

The optical properties (i.e., the complex conductivity o,(W) = a1(w) + io2(w)) have been calculated from Kramers-Kronig analysis of the reflectance data. The usual requirement of the Kramers-Kronig integrals to extend the reflectance at the low- and high-frequency ends was done in the following way. At low frequencies, the extension was done by modeling the reflectance using a Drude-Lorentz model and using the fitted results to extend the reflectance below the lowest frequency measured in the experiment. The high-frequency extrapolation were done by merging the data with results from the literature89 or by using a weak power law dependence, - ~ w-" with s ~ 1-2. The highest frequency range was extended with a power law - ~ w-4, which is the free-electron behavior limit.


Results


Room-temperature spectra

Figure 13 shows the room-temperature ab-plane reflectance of the six crystals over the entire spectral range. Note the logarithmic scale. The reflectance of each samples drops steadily (but not quite linearly) throughout the infrared, with a sort of plasmon minimum around 8000-15000 cm-1 in all cases. What is notable about the two highest T, crystals of Bi2212 and Y123 is that they show high values of reflectance over 90% for w < 1000 cm-1. For the doped samples, with reduced the carrier concentration on the CuO2 planes, the reflectance in the whole infrared region is substantially decreased. As a consequence, a few infrared-active phonons in the ab-plane are visible. However, this reduction of the carrier density has little effect on the frequency location of the plasmon minimum. It is interesting to note that there is a shoulder at around 4000 cm-1 in Y123 systems, which is probably associated with







42


excitations on the b-axis-oriented chains. This is in accord with the measurements on single-domain Y123 crystals.59

The real part of the conductivity u1(w), obtained from Kramers-Kronig analysis of the reflectance, is shown in Fig. 14. The ab-plane optical conductivity spectra of the Bi2212 and Y123 near optimal doping have several common features. There is a peak at w = 0 and a long tail extending to higher frequencies in the infrared region where a1 (w) falls as w-1, slower than w-2 decay of a Drude spectrum. At higher frequencies, we observe the onset of the charge-transfer absorption at about 14000 cm-1, which corresponds to the optical transition between the occupied 0 2p band and the empty Cu 3d upper Hubbard band. Other interband transitions also appear above 20000 cm-1. In the reduced-Tc samples, as suggested by the reflectance data in Fig. 13, there is a lot of spectral weight lost in the infrared region. Significantly, the weight lost below the charge-transfer absorption band is transferred to the higher frequencies. Note that the Y123 crystals show a bump-like structure around 4000 cm~1 on account of the excitations in the chains mentioned above. Finally, weak phonon modes, which are not completely screened by the free carriers, are seen in the far-infrared.

Additional information about the electronic structure can be extracted from the oscillator strength sum rule.90 The effective number of carriers participating in optical transitions for energies less than hw is given by



--NfEf(w) = 2mVeu1 al(w' )do', (5)
m* ire2NC
0

where m* is the effective mass of the carriers, m is the free-electron mass, V11 is the unit cell volume, and Ncu is the the number of CuO layers per unit cell. Here, we use Ncu = 2 for all measured twinned single crystals. The effective mass is taken as the free-electron value. A plot of Neff(w) per planar Cu atom is shown in Fig. 15 on a linear







43


scale. For the crystals with high dc conductivity, Neff(W) at first increases steeply at low frequencies, on account of the appearance of a Drude-like band centered at w = 0, and continues to increase in the mid-infrared region. Neff(W) exhibits a plateau in the interval between 6000 and 12000 cm-1. Above 12000 cm-1, the remaining charge-transfer excitation and higher frequency transitions contribute Neff(W). As expected, the decreasing Neff(w) over a wide frequency range was observed in the low T, samples. However, all Neff(w) curves come together above 30000 cm-1. This shows that, as reducing carrier numbers, the low-frequency spectral weight shifts to high frequency but the total weight does not change below 30000 cm-1. Indeed, the redistribution of the spectral weight in the CuO2 planes with doping have been observed for Sr-doped La21491 and oxygen-deficient Y12392,93 as well.


Temperature dependence in the infrared

The temperature dependence of the ab-plane infrared conductivity is shown in Fig. 16. The optical response of all samples is metallic, i.e., when the temperature is lowered from 300 K, there is an increase in a1(w) at the lowest frequencies, in accord with the dc resistivity. As mentioned above, for T > T, al (w) is strongly suppressed in underdoped samples over the entire infrared frequency range. Nevertheless, the conductivity below 300-400 cm-1 remains approximately Drude-like: a zero-frequency peak which grows and sharpens as temperature is reduced. The temperature dependence at frequencies above 1000 cm-1 is relatively modest; it is in fact mostly due to a narrowing of the Drude-like peak at zero frequency. Below Te, we observe that there is a transfer of oscillator strength from the far-infrared region to the zero frequency 6-function response of the superconducting condensate.94 The spectral weight lost at low frequencies in the superconducting state is large in the nearly optimally doped samples while in the most underdoped samples it is very small. It should be noted






44


that for all doping level studied, at 20 K, there remains a pronounced conductivity at low frequencies, suggesting no sign of a superconducting gap.

Figure 17 shows the real part of the dielectric function at three temperatures below 2000 cm1. The rapid decrease in ei(w) of all the samples at low frequency with decreasing temperature is an indication of the metallic behavior (characteristic of free carriers). In a purely Drude system, the zero crossing corresponds to the location of the screened plasma frequency, C, = w/fVio where e, is background dielectric associated with the high frequency interband transitions, and the plasma frequency Wp is related to the carrier density n through wp = V47rne2/m*. However, the cuprates are not simple metals, and the presence of a number of excitations in the mid-infrared will tend to shift the zero crossing to a lower frequency. Thus, estimate of carrier density should be made from Neff(w) instead of Co. As the temperature is lowered below Te, e (w) shows a large negative value, implying that the inductive current dominates over the conduction current in the superconducting state. Here, the dielectric function looks like that of perfect free carriers; el(w) = C"" - 2s/02 where wps = V47rnse2/m* is the superfluid plasma frequency and n, is the superfluid density. The reduced n, is quite evident in the doped samples in the Fig. 17.


Discussion

Low-frequency spectral functions

As noted previously, ARPES experiments72-74 on underdoped Bi2212 crystals in the normal state revealed the existence of a pseudogap in the charge excitation spectrum-a suppression of spectral weight with a residual intensity on the Fermi level. For a next step, in order to investigate the influence that the pseudogap has on the peculiar charge dynamics of the CuO2 planes, we present a complete set of temperature-dependent data in the most underdoped Bi2212 with T, = 35 K.







45


Our other undedoped Bi2212 and Y123 samples gave similar results. We emphasize two important spectral functions, the real part of the conductivity a1(w, T) and a dimensionless measure of spectral weight Neff(w, T).

Optical conductivity. The temperature evolution in al (w, T) is shown in Fig. 18. In the normal state, l (w, T) approaches the ordinary dc conductivity at low frequencies (The dc conductivity is shown on the vertical axis as filled squares). At the same time, we observe a narrowing in the far-infrared conductivity at low temperatures, whereas at higher frequency, o1(w) does not show much temperature variation. If there is indeed the formation of an energy gap at the Fermi surface in normal-state superconducting cuprates at low hole densities, from ARPES, at least in underdoped Bi2212, the corresponding optical conductivity spectrum should exhibit a bump-like structure. The situation must be similar to an interband transition like the chargetransfer band in the cuprates. Note also that the opening of a pseudogap in the electronic spectrum is clearly seen in the c-axis conductivity of Y123 and Y124.7r-77 In contrast to this, no distinct features have been observed in infrared ab-plane o1(w, T) for our underdoped Bi2212 crystals. Additionally, in underdoped cuprates which exhibit a pseudogap, there is convincing evidence that the lattice responds to this change in the electronic spectrum.95'96 In Fig. 18, there is a strong phonon resonance at - 630 cm-1 in the whole temperature range. We believe this phonon is the ordinary in-plane vibration. The phonon frequency hardens by 14 cm-1 as the sample cools from 300 to 20 K and no anomalies at either T* or T, are observed.

Spectral weight shift. We now turn to an analysis of Neff(w, T) function, which is plotted in Fig. 19 and obtained by numerical integration Eq. 5 of o1(w, T) in Fig. 18. In the normal state, the spectral weight associated with the free carriers shifts to lower frequency with decreasing temperature, on account of the sharpening of the Drude-like peak in a1(w). This is reflected in the rapid increase in the value of Nef(w, T) at low







46


frequency. A more detailed look of the temperature dependence of the low-frequency spectral weight is given in the inset of Fig. 19. We plot the difference in Neff(W, T) computed in the 300 K and other lower temperatures for w = 250, 500, 1000, and 2000 cm-1. Again, the gradual increase of the spectral weight is observed at each frequency from 200 to 75 K. If there were pseudogap to develop in the charge carrier excitation spectrum of underdoped Bi2212, as suggested by ARPES measurements, "-4 one would expect an influence on the low-frequency spectral weight from the gapping some of the carriers at particular parts of the Fermi surface. This modification of the Fermi surface should give rise to the redistribution of low frequency spectral weight. In contradiction to this expectation, we do not find any significant change in the normal-state curve as temperature is reduced, other than the already mentioned shift to lower energies. In contrast, the Neff(w, T) curve for the superconducting state does indeed show a reduction of spectral weight compared to the normal state. The missing area in the al (w, T) in the superconducting state appears in a 6-function at w = 0, and this contribution is not included in the numerical integration which yields Neff(w, T). Therefore, the difference between Neff(w, T) above and below T, is a measure of the strength of the 6 function, and is proportional to the spectral weight in the superfluid condensate.

Dielectric function models

In analyzing the ab-plane optical spectra of high-T, materials, there has been much discussion over the one-component and the two-component pictures used to describe the optical conductivity.4 In the two-component analysis, there are assumed to be two carrier types: free carriers which are responsible for the dc conductivity and which condense to form the superfluid below Tc, and bound carriers which dominate the midinfrared region. Thus, the o1(w) spectrum is decomposed into a Drude peak at w = 0 with a temperature dependent scattering rate and a broad mid-infrared absorption






47


band centered at finite frequencies, which is essentially temperature independent. An example of this approach is to fit the data to a Drude-Lorentz model dielectric function
2 N 2
JPD + ';j +, 6
w(j 2+ir SW WW2 -U-j+ FO 6
/7D j=1 J
where WpD and 1/rD are the plasma frequency and the scattering rate of the Drude component; wj, 7y, and wpj are the frequency, damping, and oscillator strength of the Jth Lorentzian contribution; and e. is the high frequency limit of e(w) which includes interband transitions at frequencies above the measured range.

The alternative, a one-component picture, has only a single type of carrier; the difference between mid- and far-infrared response is attributed to a frequency dependence of the scattering rate and effective mass. As an empirical approach one can use the generalized Drude formalism

W2

W(W + z~)

where op is the bare plasma frequency of the charge carriers, and y(w) = 1/r(w) iwA(w) is the complex memory function. The quantities 1/r(w) and A(w) describe the frequency-dependent (unrenormalized) carrier scattering rate and mass enhancement so that the effective mass is given by m*(w) = m(1 + A(w)).

A one-component model also comes from the ideas of non-Fermi-liquid behavior of the high-Te superconductors, as introduced by Varma et al.81,82 in the "marginal Fermi liquid (MFL)" theory and Virosztek and Ruvalds97,98 in the " nested Fermi liquid (NFL)" theory. In the MFL, the dielectric function is w2
'E(W) = e -' (8)
w[w - 2E(w/2)]'

where E(w) represents the complex self-energy of the quasiparticles, and the factors of 2 arise because quasiparticle excitations come in pairs. The real part of E is related to







48


the effective mass m* by m*(w)/m = 1-2 Re E(w/2)/w whereas the imaginary part of E is related to the quasiparticle lifetime through 1/r*(w) = -2m Im E(w/2)/m*(w).

The basic assumption of these theories is that there exists an anomalous charge or spin response (or both) for the cuprates. It is worth mentioning that other microscopic theories, such as the "nearly antiferromagnetic Fermi liquid (NAFL)" theory proposed by Monthoux and Pines99 and the "phase-separation model" advocated by Emery and Kivelson,'00 all lead to a similar picture. The self-energy, E, of the charge carriers (essentially the scattering rate) should take the form,


- Im E(w) { ATT, w < T (9)
irAw, o > T

where AT or A, is a dimensionless coupling constant. Hence, for W < T the model predicts a renormalized scattering rate that is linear in temperature, which agrees with the linear temperature dependence in the resistivity that is observed in nearly all copper-oxide superconductors. As w increases, reaching a magnitude of order of T, interaction of the charge carriers with a broad spectrum of excitations comes to dominate the response. This causes - Im E(w) to grow linearly with frequency, up to a cutoff frequency w, that is introduced in the model.

The functions 1/r(w), m*(w)/m, and - ImE(w) etc. can all be calculated from the Kramers-Kronig derived dielectric function. In doing these calculations, we have used the bare plasma frequency values of w,, calculated from the conductivity sumrule analysis in Eq. 5 with integration of a-i(w) up to the charge-transfer band. The values of eo are obtained from fitting the low-frequency reflectance data below the charge transfer gap by using a Drude-Lorentz model. In the following section, we will discuss the behavior of the quasiparticle scattering rate from these different points of view.







49


Quasiparticle scattering rate

Generalized Drude model. First, let us focus on the frequency-dependent scattering rate, shown in Fig. 20, extracted from the generalized Drude formalism using Eq. 7. Starting with the Bi2212 crystal with T, = 85 K, we find that the room temperature 1/r(w, T) is linear up to 2000 cm~1. When the temperature is reduced from 300 K to 200 K, the high frequency part of 1/r(w, T) gently decreases and still exhibit nearly linear frequency dependence while below 800 cm-1 the scattering rate 1/r(w, T) falls faster than linearly. The suppression in 1/r(w, T) at low frequencies is clearly resolved at lower temperatures. Similar feature has been previously observed optically and even discussed in relation to a pseudogap state.7880 At 20 K, the low-frequency 1/r(w, T) drops more sharply, although to use a Drude formula in the superconducting state does not seem correct.

Upon decreasing the carrier density in Bi2212, T, = 40, 35 K, the frequencyand temperature-dependent behavior in 1/r(w, T) is more astonishing. The absolute value of the 300-K 1/r(w, T) increases at high frequencies. Unlike the case of the nearly optimally doped Bi2212, a distinct suppression of 1/r(w, T) is observed over the whole temperature range. The position where 1/r(w, T) deviates from being the linear in o seems to move towards higher frequencies, and the depth of the normalstate threshold structure also increases as well. It is worthwhile to mention that above 1000 cm~1 the absolute value of the scattering rate in the Y 35%-doped Bi2212 is somewhat higher than that in the Pb 50%, Y 20%-doped sample. One possible explanation is that additional scattering mechanism, which originates from the baxis superlattice structure of Bi2212, is removed by the Pb doping. Nevertheless, we would like to point out that the shape of the normal-state and superconducting-state 1/r(w, T) looks very similar in these heavily underdoped Bi2212.






50


The 1/r(w, T) spectra for Y123 are shown in the lower panels of Fig. 20. We begin with the Y123 crystal with T, = 92 K. At 300 K, the high-frequency 1/r(w, T) is approximately linear, with a deviation from linearity below 800 cm-1. At lower frequencies we also observe a small upturn in the 1/r(w, T) spectra. As similar to the case of Bi2212, the scattering rate is suppressed more rapidly at low frequencies (W < 800 cm-1) when temperature is reduced. Upon entering into the superconducting state, the low-frequencies 1/r(w, T) is depressed significantly. With 15% Pr substitution (T, = 75 K), the overall magnitude in 1/r(w, T) is increased somewhat and the amount of change with temperature is diminished. In general, the 1/ir(w, T) shows similar behavior to the nearly optimal doped Y123. When the Pr content is increased to 35 % (T, = 40 K), the scattering rate is strongly enhanced at all frequencies. The frequency dependence of 1/r(w, T) is also modified as well. In particular, the slope of 1/r(w, T) becomes negative at higher frequencies, with a maximum near around 1200 cm-1. It is, moreover, remarkable that there is a resemblance in 1/r(w, T) between the spectra obtained at 20 K and at T > T.

Marginal Fermi liquid analysis. Figure 21 shows the imaginary part of the selfenergy for various doping and temperatures, calculated using the MFL formula in Eq. 8. For the nearly optimally doped Bi2212 and Y123, the 300-K - ImE(w, T) spectra increase with frequency in a quasilinear fashion though a small deviation from linearity below 400 cm-1 is observed in Y123. As the temperature is lowered, a threshold structure develops at low frequencies and becomes progressively steeper with the decrease of temperature while the temperature dependence is rather small in the high frequency part of - ImE(w, T). The difference between the room-temperature and the superconducting-state - Im E(w, T) is prominent at low frequencies. When carrier density is decreased, deviations from linear behavior appear, even at room temperature; moreover, the shape of the normal-state - Im E(w, T) becomes similar to that







51


in the superconducting state. It is important to note that the frequency scale associated with the suppression of - Im. E(w, T) does change with doping. For the most underdoped samples with T, = 35, 40 K, the normal-state depression of - Im E(w, T) occurs at w < 800 cm-1. As the doping level is increased towards the optimal, the onset frequency related to the changes of - Im E(w, T) is about 400 cm-1.

Qualitatively, as shown in Eq. 9, there are two regimes to consider for the

- Im E(w, T) function, i.e., w < T and w > T. We obtained the coupling constants AT = 0.4 0.02 and 0.5 0.1 in the regime w < T for the nearly optimally doped Bi2212 and Y123. Furthermore, from evaluation of the slopes in the region where -ImE(w,T) is linear in w, it is found that at 300 K A, = 0.20 0.01 in Bi2212 and A, = 0.26 0.05 in Y123. At 100 K these numbers are a factor of 2 larger. Note that our data is linear only below the cutoff frequency w, = 1200 cm-1. Much more interesting are the data for the underdoped crystals. The experimental

- Im E(w, T) curves level off above we, but below w, the slope is still larger than for the optimally doped specimens. In this respect, it appears that lowering the temperature of the sample would be equivalent to reducing the carrier density and, hence, to increase the coupling constant. Nevertheless, in accord with previous measurements on oxygen deficient Y123 single crystals,93 there is an increase in the quasiparticle interaction strength A, with decreasing carrier concentration. These results are difficult to understand within a MFL perspective. because they imply that the lower T, materials have a larger A,. The difficulty comes because the T, is also supposed to be determined by A,. Thus, strong coupling means larger A, and it should give rise to higher Tc. Finally, it is important to recall that the energy scale associated with the principal features in the - Im E(w, T) spectra obtained from the MFL analysis are all about two times smaller than the value in the 1/r(w, T) spectra by using KIe generalized Drude approach. This factor occurs because the MFL theory assumes







52


the quasiparticle excitation occurring in pairs, whereas a single excitation, such as a phonon or magnon, is assumed in the generalized Drude model.

Two - component picture. A completely different point of view is taken by the two-component picture. In this analysis, we have to subtract the mid-infrared absorption to obtain the Drude term or to fit to a combination of Drude and Lorentzian oscillators; given in Eq. 6. Figure 22 shows the zero-frequency scattering rate of the free-carrier or Drude contributions as a function of temperature from such an analysis. when T > Tc, 1/rD varies linearly with temperature (together with an essentially temperature-independent Drude oscillator strength) for all the doping level studied. Such a temperature linear behavior in 1/rD above T, has been observed earlierly in the optimally doped cuprates.35,37,0' We write h/rD = 2rADkBT + h/ro,02 where AD is the dimensionless coupling constant that couples the charge carriers to the temperature-dependent excitations responsible for the scattering, and shows in Table 2, the values of wpD, AD, and 1/ro. All the samples show a normal-state 1/rD linear in T, with all about the same slope, giving AD - 0.2-0.3. The fit is shown as the solid line. This is remarkable: despite the huge difference in Tc, the coupling constant AD is the same in these materials. They differ only in their intercept, which is a measure of the residual resistivity of each sample. The residual resistivity can also be seen in the data in Fig. 12. Below T,, 1/rD in all studied samples shows a quick drop from T-linear behavior, which has been pointed out previously in the optimally doped regime.35"01 More recently, a similar fast drop in 1/rD was also found in Pr-doped and oxygen reduced Y123 films using terahertz coherent time-domain spectroscopy.103,104 This striking feature seems to be a unique property of the cuprates. It is noteworthy that the low temperature values of 1/rD approach zero in the optimally doped samples as T is lowered. Although the 1/rD does not go to zero at low T in the underdoped materials, it is smaller than the extrapolated intercept 1/To of the







53


linear regime above T. This behavior could imply that the superconducting-state quasiparticle scattering rate is governed by the impurity effects. Another viewpoint is based on the node (zeros) of the gap function, and then the scattering rate reflects the response of the quasiparticle states with small excitation energies.

Table 2. Drude plasma frequency, WpD, coupling constant, AD, and the zerotemperature intercept, 1/To, for six materials.

Materials T, (K) wpD ( cm-1) AD 1/70 (cm-1)

Bi2Sr2CaCu208 85 9000 200 0.28 9

Y 35% 40 5600 200 0.20 85

Pb 50%, Y 20% 35 6100 200 0.20 185

YBa2Cu307_6 92 9800 200 0.26 2

Pr 15% 75 8700 200 0.25 135

Pr 35% 40 6800 200 0.26 252



Compare with dc transport. It is interesting to compare the scattering rate with the dc resistivity data. The most striking feature in Figs. 20 and 21 is that both the normal-state 1/-r(w, T) and - Im E(w, T) spectra show a threshold structure at low frequencies in the underdoped materials. When the doping reaches the optimal level the threshold structure is weakened. The dc resistivity in Fig. 12 of underdoped crystals is linear function in T for T > T*, but shows a crossover to a steeper slope at T < T*. If the temperature dependence of the normal-state resistivity p = (m/ne2)(1/r) is attributed entirely to the scattering rate, then the crossover behavior could be attributed to the low-frequency suppression of the scattering rate. As discussed already, this view is further supported by many experimental observations showing that the pseudogap state develops at T < T* in the underdoped compounds. However, in this connection we should remark on a discrepancy between the scatter-







54


ing rate and the pseudogap state. As shown in Figs. 20 and 21, it must be recognized that a threshold structure exists already at room temperature in the underdoped samples even though all dc resistivity curves exhibit a linear T dependence from 300 K to T*. Moreover, when a pseudogap opens, the amount of low-energy scattering decreases, implying that the absolute value of the scattering rate in the sample should be lower than that without a pseudogap state. Our experimental observations are not in accord with this expectation. First, as shown in Fig. 22, the two-component analysis shows that the linear-T behavior in 1/rD was found in all samples. Second, the decreased scattering rate is nearly the same independent of whether the pseudogap is expected or not. Third, the limited number of points and possible uncertainties specially below 100 cm-1 prevent us to determine whether the observed deviation from linearity below T* in dc resistivity data is consistent with our present results in 1/rD. However, a strong suppression in scattering, as suggested by the 1/r(w, T) and - Im E(w, T) results, is ruled out.

Superconducting response

Superconducting gap. The superconducting gap and the nature of the superconducting condensate are two fundamental quantities which characterize the superconducting state. An ordinary s-wave superconductor has a gap A in its excitation spectrum, which causes oi(w) to be zero up to w = 2A; above this frequency a1(w) rises to join the normal-state conductivity.105 Furthermore, structure in a1(w) at 2A + S1o reflects peaks at flo in the effective phonon-mediated interaction a2F(I), and a detailed measurement of o1(w) can in principle be determine a2F(II).106 Thus it was hoped that infrared measurements of a1(w) for the high-Tc superconductors would provide similar information on both the gap and the pairing mechanism. However, in spite of considerable of data on high-quality samples, there is no consensus yet whether a superconducting gap is observable in the infrared spectrum. For several







55


reasons, the search for evidence of a superconducting gap in high-T, materials has proven difficult.

First, gap anisotropy can lead to broadening of the absorption edge and a diminution of the gap structure in the optical conductivity. ARPES of Bi2212 implies that the gap is highly anisotropic in k-space. The corresponding optical conductivity spectrum would not exhibit a sharp onset. Second, if one interprets the oj (w) data based on the two-component model as described in Eq. 6, then the presence of the second component (mid-infrared band) can overlap and possibly mask any gap absorption. In this view the quasiparticle scattering rate may be low relative to the superconducting energy gap (1/rD < 2A) so that one is in the clean-limit in which almost all of the free carriers condense to form the superfluid and little spectral weight is left for transition across the gap. In principle, one can experimentally test the second point by enhancing the scattering rate to produce optimum circumstances for the observation of the 2A onset in uj(w). Doping is an important method to study this possibility.

As shown in Fig. 15, the superconducting state conductivity of the nearly optimally doped samples is finite and no superconducting gap exists down to the low frequency limit of our measurements, consistent with previous reflectance3,107 and direct absorption data'08. The finite absorption in the superconducting state is not due to experimental problems or sample-to-sample variation, suggesting that it is a fundamental characteristic of the fully doped materials. One of the possible origins is the tail of the mid-infrared absorption in the two-component model. The other possibility could be associated with nodes in the superconducting gap, such as might occur in the d-wave superconductor.109'" For the most underdoped Bi2212 crystal (T, = 35 K), shown in Fig. 18, there is no evidence of a gap in the superconducting spectra. The effect of doping on the optical absorption spectrum in the gap region does







56


not produce dirty-limit behavior as seen in conventional superconductors-an onset of absorption at 2A. Instead, a new low-frequency, Drude-like, absorption appears in the superconducting state, taking spectral weight away from the superconducting condensate. This observation could be also due to the unconventional nature of the response of the high-T, superconductors. If a d-wave gap is a possible scenario, the low-frequency absorption will be enhanced in a dirty sample.

Superfluid density. Although there is still a lot of controversy about the experimental data and their interpretations regarding optical studies the superconducting gap in the cuprates, the spectral weight or oscillator strength of the superconducting condensate is given less ambiguously from infrared measurements. A superconductor has a low frequency a1 (w) that is a 6 function at w = 0; in turn, this S function gives (by Kramers-Kronig) a contribution to el(w) of e1(w) = e, - w2/2. Thus the w2 component of the very low-frequency e1(w) measures the superfluid density directly and is equivalent to a penetration depth AL experiment. Figure 23 shows e1(w) plotted against w-2; a linear regression of the straight line yields wpS. Results for all our samples are listed in Table 3.


Table 3. Plasma frequency of the condensate, wpS, and the penetration depth,
AL, at 20 K.

Materials Tc (K) wps ( cm-1) AL (A)

Bi2Sr2CaCu208 85 8800 200 1860

Y 35% 40 4100 t 400 4130

Pb 50%, Y 20% 35 3700 400 4910

YBa2Cu30O_6 92 9200 200 1720

Pr 15% 75 7700 400 2110

Pr 35% 40 4200 400 4260







57


The superconducting penetration depth is a related parameter, which we are naturally led to associate with the superfluid density. It is a direct measure of the density of carriers n, condensed in the superconducting state and through its temperature dependence, the symmetry of the superconducting order parameter can be discriminated. The penetration depth is usually determined by the experiments of muonspin-rotation (pSR), DC magnetization, and surface impedance in the microwave and millimeter wavelength region. The later two methods, while yields the temperature dependence of the penetration depth with great accuracy, generally can not be used to obtain its absolute value. In the case of infrared measurements, the penetration depth can be found from Kramers-Kronig analysis of the reflectance data, which gives the imaginary part o2(w) of the complex conductivity as well as the real part ou(w). 02(w) is directly related to a generalized AL(w):


[r21 1/2
A L(w) = [ 2 12(10) 47rwO2(w)

where c is the light speed. Equation 10 is a direct consequence of the 6-function in the real part of the conductivity at w = 0. The frequency-dependent penetration depth of all the samples at 20 K is shown in Fig. 24. Note that a smaller AL corresponds to a larger superfluid density. AL(w) is almost frequency independent at low temperatures in the samples near optimal doping, suggesting that the superfluid response dominates the other contributions to the conductivity. In contrast, for the underdoped compounds, AL(w) shows some frequency dependence below 300 cm~1 is an indication that not all of the free carriers have condensed into the 8 function.

Alternatively, the conductivity sum rule provides a good estimate for the strength of the 6-function peak,

2 00
A2(0) = 8 ( - .(u))d(
0







58


where Oin(w) and uj,(w) are the real parts of the complex conductivity at T ; T, and T < Te, respectively. Equation 11 states the spectral weight lost at low frequencies in the superconducting state has been transferred to the zero-frequency 6-function response of the superconducting condensate. This missing spectral weight from the sum rule is indicated by solid squares in Fig. 24. The values of penetration depth of all samples obtained by Eq. 11 are displayed in Table 3. Generally speaking two estimates for AL in Eqs. 10 and 11 agree within about 10%. The penetration depth is related to the plasma frequency of the condensate by, AL = c/Wps. The values of WpS obtained directly from the dielectric function el (w) or through the sum rule agree well.

Spectral weight above and below Tc. We now turn to a comparison among the various contributions to o1(w), above and below T. We have used finite-frequency sum-rule analysis in Eq. 5 and then calculated the effective number of carriers per planar Cu atom in the low frequency region below the charge-transfer gap as Ntet, the Drude or free carrier part (from two-component analysis) as NDrude, and the superconducting condensate weight as N.. Results for our Bi2212 and Y123 systems together with oxygen doped La2CuO4.12111 (La214(0))and fully optimal T12Ba2CaCu208112 (T12212) are summarized in Table 4. N is also shown as a fraction of Net~ and NDrude. Notably, there is an "universal correlation" between the numbers of carriers and the transition temperature. This link holds whether one considers the number of carriers in the superfluid or the total number of carriers. In Fig. 25 we plot T, versus ntot for high-Tc superconductors, where nitt = Ntot - NCu/Vcei-." One Bi2212 sample has T = 68 K by Ni 4.3% substitution. In addition, one point has also been included for the a superconductor oxide that is not based on CuO2 planes, Bal_,KBiO3 (BKBO) with T, = 28 K.114 All of the data points follow an approximately common line. In the conventional superconductors an increased carrier density normally leads to an







59


increased T,. A similar trend has been observed for the cuprates at the doping level in the underdoped and optimal doped regime. Interestingly, a recent study15 on the optical conductivity of high-T, superconductors from underdoped to overdoped range points out that in the underdoped regime progressive doping indeed increases the low-frequency conductivity spectral weight while this trend does not continue to the overdoped part of the phase diagram. It is argued that there is an increase in the carrier density as T, is increasing, and overdoping decreases T, but does not lead to an increase in the total number of carriers. Another important point from the values of Ntot is that in a simple rigid-band picture, the total number of doping carriers corresponds to the volume enclosed by the Fermi surface. This interpretation, however, runs into a discrepancy between optical and photoemission determinations of carrier number. Recent ARPES measurements of Bi2212116 ranging from underdoped to overdoped infer large Luttinger Fermi surface, consistent with Net~ = 1 + x where x is the dopant concentration. In contrast, optical measurements imply that Net~ = x and we always see small Fermi surface for all doping levels studied.

Figure 26 shows the relation between T, and n, where n, = N, - NcuIVcelu.3 The most striking finding in the plot is that for the underdoped and optimally doped cuprates (filled symbols) the superfluid density increases roughly proportionally to the transition temperature. Our optical data points follow what is generally referred to as the Uemura line. These results suggest that, regardless of charge or impurity doping, it is the parameter n, that determines T, of the cuprate superconductors. As is well known from the pSR measurements (open symbols), there is a "universal correlation" between T, and n, in many cuprate superconductors: T, increases linearly with n, (solid line) with increasing carrier doping in the underdoped region, then shows saturation in the optimum-Tc region.117'11 In the overdoped Tl2Ba2CuO6 (T12201) systems, both T, and n, decrease (dashed line) with increasing hole dop-







60


Table 4. Effective number of carriers per planar Cu atom.

Materials T, (K) Not NDrude N., N% NDrde

La2CuO4.12 40 0.14 0.035 0.028 20 80

Bi2Sr2CaCu208 85 0.38 0.105 0.092 24 88

Y 35% 40 0.21 0.040 0.020 8 50

Pb 50%, Y 20% 35 0.23 0.050 0.017 7 34

YBa2Cu307_6 92 0.44 0.093 0.082 19 89

Pr 15% 75 0.38 0.073 0.054 14 74

Pr 35% 40 0.25 0.045 0.020 8 44

Tl2Ba2CaCu208 110 0.54 0.13 0.115 21 88

Typical uncertainties 2 .03 .01 .01 1% 4%


ing,119,120 bringing the trajectory in the T, versus n, back to the origin. We are presently unaware of any optical analysis on the evolution of superfluid density in the overdoped cuprates, so this subject will be addressed in future work. Finally, considering the superconducting condensate fraction in Table 4, we found that in all optimally doped materials, about 20-25% of the total doping carriers joins the superfluid; about 75-80% remains ar finite frequencies. Furthermore, if a two-component picture is adopted, then nearly 90% of the free-carrier spectral weight condenses. In other words, the oscillator strength of the 6-function is essentially the same as the Drude-like peak of the normal state, which is a clean-limit point of view. These results also indicate that the large portion of spectral weight in the normal state condenses below T, in the optimally doped samples, while the superconducting condensate in the underdoped materials is rather small.







61


Summary

In summary, the ab-plane optical reflectance of single crystals of Bi2212 and Y123 has been measured over a wide frequency and temperature range. Substitution of Y for Ca atom in Bi2212 and Pr for Y atom in Y123 allowed us to study the doping range from heavily underdoped to nearly optimally doped. We have examined a variety of spectral functions from Kramers-Kronig analysis of the reflectance data. With the reduction of carrier concentration on the CuO2 planes, we observe there is a lot of spectral weight lost in the infrared conductivity. The weight lost below the charge-transfer absorption band is transferred to higher frequencies. We have also presented a complete spectral investigation of the most underdoped Bi2212 with T, = 35 K. Emphasis has been placed on the features in the real part of conductivity 011(w, T) and the development of the spectral weight Neff(w, T), as the temperature of sample changes from above T* to below the critical temperature Tc. We find that the conductivity below 300-400 cm1 is approximately Drude-like, a zero-frequency peak which grows and sharpens as temperature is reduced. At the same time, the spectral weight associated with the free carriers shifts to lower frequencies. It is difficult to relate our experimental observations to the normal-state pseudogap phenomenon.

Considering the important role that quasiparticle damping has played in discerning the normal-state psedudogap features, we derive the scattering rate from both the one-component and the two-component pictures. In one-component analysis, our results have been treated within the framework of the generalized Drude model and the marginal Fermi liquid theory.81,82 The appearance of low-frequency depression in the scattering rate spectrum (from previous measurements78-80 as well as those reported here) signals entry into the pseudogap state. The energy scale associated with the principal features in 1/r(w, T) and - Im E(w, T) shows a factor of 2 different. The frequency scale associated with the suppression of - Im E(w, T) does change







62


with doping. For the most underdoped samples with T, = 35, 40 K, the normal-state depression of - Im E(w, T) occurs at w < 800 cm-1. As the doping level is increased towards the optimal, the onset frequency related to the changes of - Im E(w, T) was found to be 400 cm-1. An alternative approach is to consider the zero-frequency 1/rD from free-carrier contributions. We find that for all the samples studied, when T > Tc, 1/rD varies linear with temperature and decreases quickly below T. 1/r from inelastic scattering process puts all the samples in the weak-coupling limit (AD ~ 0.2-0.3). We suggest that the pronounced features in the scattering rate spectrum are related to the manner in which the data are analyzed (one- vs. two-component). It is a delicate question to ask which analysis, one-component or two-component, is more appropriated in our present study.

In the superconducting state, some of the finite frequency oscillator strength in a1(w) is removed by the superconducting transition. A finite low-lying conductivity remains below T. There is no convincing evidence of superconducting gap absorption in our spectra. In the case of the materials with near optimal doping, the absence of a superconducting gap can be explained in one of two ways: a clean-limit picture in the two-component model or the presence of an unconventional gap with nodes somewhere on the Fermi surface. However, our underdoped (dirtier) samples again show no sign of a gap, which favor the latter argument. In determining the amount of oscillator strength that condenses into the 6-function at w = 0, we obtain a good agreement of the values of superfluid density from the missing area by sum-rule argument with WpS, or through the superconducting penetration depth AL. The spectral weight lost at low frequencies in the superconducting state is large in the nearly optimally doped samples; a sum-rule evaluation finds that about 20-25% of the total dopinginduced carriers in is the 6 function. In contrast, in the most underdoped samples the superfluid density is very small. We have also found that there is an "universal







63

correlation" between the numbers of carriers and the transition temperature. This link holds whether one considers the number of carriers in the superfluid or the total number of carriers. Our optical results are significant and consistent with the evidence from pLSR measurements: T, scales linearly with n, in many underdoped and optimally doped cuprates.







64


1 .0 F -7 -r ' ' ' | ' ' ' ' | ' ' '
. ___ Bi2212
A Pb 50%, Y 20%
0.8


E
o 0.6


E
0.4


0.2


0.0
_ m Y1 23t Pr 15%
0.8 Pr 35%


E
o 0.6


E
o, 0.4


0.2


0.0
0 50 100 150 200 250 300
Temperature (K)



Fig. 12 Temperature dependence of the ab-plane resistivity for Y-doped
Bi2Sr2CaCu208 and Pr-doped YBa2Cu3O7.-6 single crystals, measured by a four-probe method. A characteristic change of slope dp/dT at temperature T* is marked by arrows.







65


Photon
1


Energy (eV)
0.1


10000 100
Frequency


1000 (cm )


1


10000


Fig. 13 The room-temperature ab-plane reflectance of six crystals over the
entire frequency range.


0.1


1.0


0.6


a,
C-,

.4
C, ci~

a,


- Y1 23
T300 K







A




Pure\
Pr 15%\
___._ ___ ._ Pr 35% '


Bi2212
T =300 K










-\


Pure
____ _Y 35%
- - - -- Pb 50%, 20%


0.4


0.2


0.0' 10


0


1000


. . . I I I I I I I . I I I I I . I . I I I I I I


I


I


0.8


. . I . 1. 1.1


I I . ..-I








66


5000


4000 H


0.1


Photon
1


B1221 2 T = 300 K


Pure Y 35% Pb 50%, Y 20%


- 7



- -


Energy (eV)
0.1


Y123 T = 300


K
Pure Pr 15% Pr 35%


---I-K-


1000


10000 100 1000
Frequency (cm~)


10000


Fig. 14 The real part of the optical conductivity a1(w) obtained by KramersKronig analysis of the room-temperature reflectance presented in Fig. 13.


3000


2000


C: 3_.


b


1000


100


1


..


' ' ' ' ' ' ' i I '


n '







67


2


Photon Energy (eV)
3 0 1


I I I . I I I I I I I


K
Pure Y 35% Pb 50%, Y 20%


Y123 T =300


/

/
7

7'

77'
-7

77
7 7'
- / 7"

/ 7'
- / /
/
/ I


10000 (cml)


2


Bi221 2
T = 300

1.00 -


0.75 0.50 0.25 0.00
0 10000 20000


Frequency


Fig. 15 The effective number of carriers per planar Cu atom Neff(W) obtained
by the integration of o1(w) up to a certain frequency, as described in
Eq. 5.


0


1.25


1


2


3


K
Pure Pr 15% Pr 35%


.4
0
z


20000


30000


. I . I . I






68


TC = 35 K
(Pb 50%, Y 20%)


Bi2212 TC = 40 K (Y 35%)


~*1 7,.


1000


0


TC = 40 K (Pr 35%)


1000


0


Y123
TC = 75 K (Pr 15%)


-I


N


I II I


1000


0


1000
Frequency (cm~1)


0


1000


2000


Fig. 16 The far- and mid-infrared optical conductivity of six samples at 20,
100, and 300 K. The symbols show the dc conductivity values.


6000


4000 H


E


2000


300 100
20 K


- 7


TC = 85 (Pure)


1000


K


2000


0


0


6000


4000 H-


TC = 92 K (Pure)


E


2000'


0


0


" -


-


K
K


-


I I


I

















300 K 100 K20 K


I!


69


T = 35 K
(Pb 50%, Y 20%)


Bi2212 TC = 40 K (Y 35%)


TC = 85 K (Pure)


w 'I-,


/

/ 'I


-1000





-2000


1000


0


T = 40 K (Pr 35%)


1000


/


- -


1000


0


Y123
TC = 75 K (Pr 15%)


L


0


1000
Frequency (cm~1)


1000


TC = 92 (Pure)


/

/

-I

I I


0


1000


Fig. 17 The real part of the dielectric function el(w) obtained by KramersKronig analysis of the reflectance data. The data shown are from w
100 to 2000 cm-1 at 20, 100, and 300 K.


I I


0


0


2000


K


:3


-1000


-2000


0


2000


- 1 1 1 1


v_.






70







Photon Energy (meV)
0 50 100 150 200
3000

Bi2212 TC 35 K
300 K 200 K 2000 -150 K
] 100 K 75 K
20 K



1000






0 '
0 500 1000 1500 2000
Frequency (cm-)









Fig. 18 The infrared optical conductivity for Y-doped Bi2Sr2CaCu208 (T, =
35 K) at temperatures between 20 and 300 K. The dc conductivity values are indicated by the symbols. We also plot the results of other studied
samples.






71


Photon Energy (meV)
0 50 100 150 200
3000

- Bi221 2
TC =40 K
300 K
200 K
2000 --- 150 K
100 K
75 K
20 K



1000






0 '
0 500 1000 1500 2000
Frequency (cm1)


Fig. 18-continued






72


Photon Energy (meV)
100 150


4000







0
~~'2000






C


0


1000
Frequency


Fig. 18-continued


0


6000


50


200


Bi221 2 TC 85 K
300 K 200 K 150 K
--_100 K
60 K 20 K








~' '


500


1500


(cm 1)


2000






73








Photon Energy
100


(meV) 150


1000
Frequency


(cm1 )


Fig. 18-continued


0


3000


50


200


E
0


2000 1000


SY1 23
TC =40 K
300 K
A - 200 K
----- - 150 K
-- -_ 100 K ... 50 K
f 20 K




\-.'--


0


0


500


1500


2000


i






74







Photon Energy (meV)
0 50 100 150 200
6000
Y1 23 TC =75 K 300 K
- - - 200 K
150 K
4000 - 100 K
.... 50 K
_ _ _ 20 K




2000






0 '
0 500 1000 1500 2000
Frequency (cm )


Fig. 18-continued







75


Photon Energy
100


1000
Frequency


(meV) 150


(cm )


Fig. 18-continued


0


50


200


SY123
TC =92 K
300 K 200 K 150 K
S100 K
60 K
_ _ _ _ 20 K


OUUU


4000


2000






0


0


500


1500


2000







76


Photon
100


Energy (meV)
150


Bi221 2 T0 =


35 K


-___ 300 K
__ 200 K
150 K
___ 100 K
75 K 20 K


500


50


100 150
T (K)


z T (K~









I I I I I I


0


0
0

z
I-


30 15


200 250


1000
Frequency


1500


(cm~1 )


Fig. 19 The partial sum-rule spectrum per planar Cu atom, Neff (w, T), for
Y-doped Bi2Sr2CaCu208 (T, = 35 K) at temperatures between 20 and 300 K. The inset shows the difference in Neff(w, T) computed in the 300 K and other lower temperatures for w = 200, 500, 1000, and 2000 cm-1.


0


0.20


50


200


0.15 K


- 250 cm -1
- A 500 cm-1
- x 1000 CM
* 2000 cm~
A
-


- *


0.10


0.05


0.00


0


2000


' ' ' ' ' ' ' ' '


I I I


' '


n I







77


0


Bi2212 TC = 40 K (Y 35%)


1000


Y123
T= 75 K (Pr 15%)









F-


0


1000
Frequency (cm-)


TC = 85 (Pure)


0


K


II


1000


2000


T= 92 K (Pure)


0


1000


2000


Fig. 20 The temperature-dependent quasiparticle scattering rate 1/T(w, T)
obtained from the generalized Drude model in Eq. 7 for Bi2Sr2CaCu208
and YBa2Cu307_b at several doping levels.


6000


T( =5 (Pb 50%,


35 K Y 20%)


4000


E
Q-


300 K 200 K 150 K 100 K
20 K

~~~~----


2000


0


0


1000


T = 40 K (Pr 35%)


W -


6000



4000 2000


E


0


0


1000


' ' '
I


'


- '


- -


I


-



- ~


~ . --







78


TC = 35 K
(Pb 50%, Y 20%)


1000


Bi2212 TC = 40 K (Y 35%)


(Y3 ' (Pre
- - '


0


1000


T = 85 K
(Pure)


1000


0


Y123
T = 75 K (Pr 15%)


1000
Frequency (cm1)


T = 92 K (Pure)


0


1000


Fig. 21 The imaginary part of the self-energy - Im E(w, T) obtained from the
marginal Fermi liquid theory in Eq. 8 for various doping and temperatures.


4000


E
U


E
T


2000


I I


300 K 200 K
_ ___. 150 K 100 K
-_ 20 K


0


0


4000


T = 40 K (Pr 35%)


2000


E




E


II I I I


I I


2000


0


0


1000


0


2000


I I --


'
|


,





'


- -


- -







79


TC = 35 K
(Pb 50%, Y 20%)


Bi2212 T0 = 40 K (Y 35%)


T = 85 K (Pure)


I II I , I , * I . I I I . I I I I I j I . ,


- ~
- -


100 200 300 100Y12S00 300 100 200 300

T= 40 K T =75 K T =92 K
(Pr 35%) (Pr 15%) (Pure)
S I I . I . I . , . I . i






I I I I ~-


0 100 200 300


100 200 300 Temperature (K)


100 200 300


Fig. 22 The zero-frequency scattering rate 1/rD of the Drude contribution
from the two-component fit of Eq. 6 to the optical conductivity. The straight lines show a linear fit to the temperature dependence of 1/Tjj
above T.


800 600


400


E
U


200


0


C


E
~U


800 600


400 200


0


.


. . . . .
i i

-
-









I







80


Bi2212 TC = 35 K TC = 40 K TC = 85 K
(Pb 50%, Y 20%) (Y 35%) (Pure)
0





-4000 20 K fit


-8000
0.0 0.5 0.0 0.5 0.0 0.5 1.0


T - ~ I,


Y123


IC=4KT = 75 K T = 92 K
0 (Pr 35%) (Pr 15%) (Pure)





-4000





-8000 ' ',,
0.0 0.5 0.0 0.5 0.0 0.5 1.0
(Frequency) 2 (cm2) (10-4)



Fig. 23 The real part of the dielectric function (dashed line), plotted against
w-2 at 20 K. The range of the data shown is 500-100 cm-1. The linear
fits are shown by the solid lines.


Z3








81


40


I I I I I
Bi221 2 T = 20 K
Pure Y 3
Pb


Photon Energy (meV) 30 120 40


5%
50%, Y 20%l


Xj~ ~ - -


80


Y1 23 T = 20 K


Pure Pr 15% Pr 35%


I


Iwo


I

I


0 200 400 600 800 0 Frequency


(~- ~~


Ii II


200 (cm-)


400 600 800


Fig. 24 The frequency-dependent superconducting penetration depth AL(W)
obtained from Eq. 10 at 20 K. The values of AL(0) from the sum-rule
analysis of Eq. 11 are indicated by the symbols.


I


120


0
6000


I


4000


2000


0


1000


I


I I I


' ' ' '


' I I


I I


I I I I I I I I - I t I I I


--------






82


160


140 120 100 80


C.)
H-


60


40 20


0


0


2

ntot (10 21


4
cm-3)


6


Fig. 25 The transition temperature T, as a function of ntot for
Bal,KBiO3 (cross),'14 La2CuO4.12 (circle),"' Bi2Sr2CaCu208
(square), YBa2Cu307_6 (triangle), and T12Ba2CaCu20 (diamond)."2
The solid line is a guide to the eye.


x BKBO
- S La214(O)
* Bi2212
A Y123
* T12212


A

A




- A
-U






83


160

x BKBO
140 La214(0)
* Bi2212
A Y123
120 T1221 2
o La214
100 A Y123
T12201

80


60


40 720


0 '
0 2 4 6 8 10 12
ns (1020 cm-3)


Fig. 26 T, plotted a function of n. Cross: Bai_.KBiO3,14 filled
circle: La2CuO4.12,11 filled square: Bi2Sr2CaCu208, filled triangle: YBa2Cu3O7._, and filled diamond: T12Ba2CaCu2O8112 from infrared measurements. Open circle: La2-zSrCuO4, open triangle YBa2Cu307_6, and open star: Tl2Ba2CuO6 from pSR measurements.117-120 The solid curve is the universal Uemura line.'17 The dashed
curve is based on pair-breaking model calculation.120













CHAPTER IV
OPTICAL STUDY OF UNTWINNED
(Bii.57Pbo.43)Sr2CaCu2O8+6 SINGLE
CRYSTAL: AB-PLANE ANISOTROPY


Introduction

The dimenionality of the cuprate superconductors is an important issue, related as it is to the basic picture (Fermi liquid, non Fermi liquid, etc.) that one has for their electronic structure. It is widely accepted that the key to the high-T, superconductors problem is hidden in the CuO2 planes, which are a common feature to all of the cuprates. Many theoretical models which attempt to explain the mechanism responsible for superconductivity are two dimensional. Thus is a reflection of the assumption that the only active pieces of the crystals are the CuO2 planes, with the rest of the material layers serving only structural or charge-balance functions. Experimentally, most analyses, such as dc resistivity,121-123 the infrared conductivity31,59,93,108,124-126 and the penetration depth,32 have been performed on single-domain YBa2Cu307_6(Y123). Much of the observed anisotropy of Y123 can be attributed to the quasi-one-dimensional CuO chains; their presence prevents determining whether the CuO2 planes themselves have any intrinsic properties. In contrast, Bi2Sr2CaCu208 (Bi-2212) provides a better opportunity to study the issue of the electronic structure of the CuO2 planes because there are no chains in these Bi-based compounds.

A considerable investment was thought that a possible way of investigating the electronic structure of the high-T, superconductors was to measure the size and shape of the Fermi surface.127 Recent angle-resolved photoemission spectroscopy (ARPES) is continuing to make important contributions towards understanding the electronic


84







85


structure of the normal as well as the superconducting state of the high-Te materials. The method has been applied to map the Fermi surface of Bi-2212 completely.74,116,128-135 Normal state spectra74,132 show an anisotropic in-plane Fermi surface. There is only one peak corresponding to the main planar CuO2 band; no resolvable Bi-layer splitting is seen above Tc. All other spectral features have been attributed either to umklapp band related to the structural superlattice, or to shadow band based on the presence of antiferromagnetical spin fluctuations in the metallic state.136 Another important feature of Bi-2212 Fermi surface is that the observation of a large Luttinger Fermi surface containing 1 + x holes, where x is the hole doping.74,116,128 With decreasing temperature, ARPES is able to determine the magnitude of the superconducting gap (Ak) on different parts of the Fermi surface. The existence of a substantial gap anisotropy in Bi-2212 with respect to k indicates that the superconducting order parameter is not a simple s-wave.135,137,138 Indeed, the abplane anisotropy of the superconducting gap in Bi-2212 has been confirmed by other measurements including tunneling139 and Raman scattering.140 Also, the previous report by Quijada et al.107'141 has found that the polarized reflectance of the ab-plane of single-domain Bi-2212 crystals is anisotropic above and below Tc.

Despite these extensive spectroscopic studies, questions still exist regarding the presence of the structural superlattice, which necessarily affects the experimental data on the highest quality Bi-2212 samples. A general question arises as whether the anisotropy of ab-plane in Bi-2212 is intrinsic, or being probably due to the superstructure of the Bi-O plane. This gives a motivation to study Pb-doped Bi-2212 single crystals since the superlattice modulation disappears (or changes) gradually as bismuth is replaced by lead:142 a structurally simplified situation and through this clarity on the influence of the modulation on the electronic structure of the CuO2 planes. In a recent ARPES study of Pb-doped Bi-2212,143 it was shown that







86


the Fermi surface still has orthorhombic symmetry. We are pursuing experimentally the measurements of the ab-plane polarized reflectance spectra above and below the superconducting transition temperature in a high quality, untwinned single crystal of (Bi1.57Pbo.43)Sr2CaCu2O8+6 [Bi(Pb)-2212. Infrared spectroscopy is a powerful tool on the aspect of high-T, superconductors.21 Unlike the surface sensitive technique of APRES (approximately 15 A in the cuprates), infrared light probes the bulk properties of the materials. Optical methods provide information on the dynamics of the free carriers, the nature of the charge-transfer and other low-energy excitations, the superconducting gap (in principal), phonons and other aspects of the electronic structure. Furthermore, using polarized reflectance measurements we have been able to obtain the optical response along the principal axes of the crystal. Interest has focused mainly on the investigation of the dielectric tensor component (a- vs. b-axis) of Bi(Pb)-2212. In addition, we will compare our data on Bi(Pb)-2212 to previous optical results on Bi-2212 by Quijada et al.107'141


Experimental

The Bi(Pb)-2212 single-crystal sample was prepared by a standard flux-growth technique.144"145 The crystal was thin platelet with smooth and uniform surface and typical dimension 2.5 x 3 x 0.2 mm3. The as-grown crystal was used without any annealing. The superconducting transition temperature was obtained by means of ac magnetization measurement. The T, onset value for this crystal was found to be 80 K with ATc = 2 K. Characterizations of dc resistivity, ac susceptibility, Xray diffraction and low-energy electron diffraction (LEED) have been performed on similar samples grown in the same way.143 The crystal structure of undoped Bi-2212 is pseudo-tetragonal (I4/mmm - D4h space group). There is a displacive modulation of the Bi-O sublattice along the b-axis with a wavelength ; 5 |&j'"' 147 (taking |bi ; 5.4 A). Note that in Bi-2212 structure the a and b axes are along the Bi-O-Bi







87


bonds, and correspond respectively to the F-X and T-Y directions in the Brillouin zone. They are nearly 450 from the Cu-0-Cu bond (F-M direction). By contrast, the modified modulation wavelength along the b-axis in Bi(Pb)-2212 increases to about 131b|, as was confirmed by LEED.143 The LEED pattern exhibited an almost 1 x 1 structure for Bi(Pb)-2212, whereas it was a 4.6 x 1 pattern for undoped Bi-2212. The change of modulation wavelength with Pb doping suggests that Pb really enters into the Bi sites. Furthermore, X-ray diffraction and LEED measurements143 indicate no structural change in the CuO2 planes for Bi(Pb)-2212 samples. It is worth mentioning that the recent observation by Winkeler et al.148 which found that Pb doping increases the c-axis interlayer coupling in compared to the undoped Bi-2212. The out-of-plane resistivity p,(T) decreases by four orders of magnitude. The temperature behavior changes from semiconductor-like to metallic. However, it is generally believed that Pb doping does not perturb the electronic states critical to superconductivity in this system,149 and the electronic structure of Bi(Pb)-2212 is close to that of undoped Bi-2212.

The polarized reflectance was measured at near-normal incidence. Far-infrared and mid-infrared measurements were carried out on an Bruker 113v Fourier-transform infrared spectrometer using a 4.2-K bolometer detector (80-600 cm-1) and a B-doped Si photoconductor (450-4000 cm-1). Wire grid polarizers on polyethylene and AgBr were used in the far- and mid-infrared, respectively. A Perkin-Elmer 16U grating spectrometer in conjunction with both thermocouple, PbS, and Si detectors was used to measure the spectra in the infrared to the ultraviolet (1000-32000 cm-1), using wire grid and dichroic polarizers. The room-temperature polarized reflectance in the visible frequency region (14300-23800 cm-1) was also made using a Zeiss MPM 800 Microscope Photometer with grating monochrometer, especially designed for spot measurements. We measured on the shiny, smooth, and well-reflecting spots with







88


a size about 50 x 50 jm2 by using a magnification of lOx and 20x. For lowtemperature measurements, the sample was mounted in a continuous flow helium cryostat equipped with a thermometer and heater near the cryostat tip, regulated by a temperature controller. Calibration of the absolute value of the reflectance was done by coating the sample with a 2000 A film of Al after measuring the uncoated sample. The spectra of the uncoated sample were then divided by the obtained spectrum of the coated sample and corrected for the known reflectance of Al. The accuracy in the absolute reflectance is estimated to be 1%. However, the accuracy of the anisotropy of the reflectance (i.e., the difference between a and b results on the same sample at the same temperature) is better than 0.25%.

The optical properties (i.e., the complex conductivity o(W) = 1(w) + i2(w) or dielectric function e(w) = 1 + iff7w) ) have been calculated from Kramers-Kronig analysis of the reflectance data.90 Because a large frequency region was covered, Kramers-Kronig analysis should provide reasonably accurate values for the optical constants. To perform these transformations one needs to extrapolate the reflectance at both low and high frequencies. At low frequencies the extension was done by modeling the reflectance using the Drude-Lorentz model and using the fitted results to extend the reflectance below the lowest frequency measured in the experiment. Between the highest-frequency data point and 40 eV, the reflectance was merged with the undoped Bi-2212 results of Terasaki et al.150; beyond this frequency range a free-electron-like behavior of w-4 was used.







89
Results and Discussion
Polarized reflectance

In Fig. 27 we show the room-temperature polarized reflectance of Bi(Pb)-2212 and Bi-2212107'141 (inset) crystals measured over a wide frequency range. Surprisingly, the anisotropy features of the spectra of Bi(Pb)-2212 and Bi-2212 are almost the same. The a-axis reflectance is higher than the b-axis reflectance by 1-2% in the far-infrared region. As the frequency increases, the reflectance falls off in both polarizations. The position of the plasma edge for the b-axis polarization occurs at slightly lower frequency than in the a-axis direction. The splitting is estimated to be around 500 cm-1 in contrast to the studies,31,59,93,108,124-126 on untwinned Y123, which showed a significant difference (~ 5500 cm-1) in the a and b axis plasma edge. The larger plasma edge along the b direction in the Y123 system has been attributed to the presence of CuO chains along the b axis. However, neither Bi-based compounds has chains, indicating that the electronic excitations within either the CuO2 or Bi-O planes being themselves anisotropic. Our results for Bi(Pb)-2212 favor the anisotropy introduced by the CuO2 planes since the displacement modulation along the b axis is partly suppressed by substitution Pb for Bi. We have also found that for both samples the reflectance is substantially higher in the b axis above the plasma minimum.

In addition, there are two electronic absorption bands at ~ 2.3 and 3.8 eV in both polarizations. There is general agreement that the broad band at -2.3 eV is associated with 0 2p -- Cu 3d charge-transfer excitations in the CuO2 plane. But identification of the -3.8 eV excitation remains controversial."'-"' So far, there are two possible candidates for the origin of this band. One is the optical transition within the Bi202 layers,e.g., between Bi 6p and 0 2p, and the other in the CuO2 layers. Of course, it is possible that both excitations overlap with each other. As seen in the inset of Fig. 27 for the Bi-2212, the absorption band at ~ 3.8 eV is more pronounced along b than in the a direction. The difference is smaller in Bi(Pb)-2212.







90


Naturally, it would be preferable to think that the 3.8 eV peak could be associated with transitions occurring in the Bi-O layers because of the substitution of Pb in Bi2212 having a strong influence on the incommensurate modulation along the b axis. However, the discrepancy may also arise from the difference in the oxygen doping level of samples. At the moment our optical data is not enough to distinguish such electronic transitions from each other.

One could question whether the anisotropy in polarized reflectance spectra is inhomogeneity of high-Tc samples parallel to the c axis. Such inhomogeneity could result in surface steps with different structure or composition. We regard such effects as extremely unlikely in the present study. In all, the Bi(Pb)-2212 and Bi-2212 crystals are grown by different groups. We have examined on shiny, smooth and wellreflecting surfaces in all measurements. The high degree of anisotropic reproducibility in visible frequency region was also obtained by using Microscope measurements. On the other hand, we must note that similar polarization dependence has been seen in earlier ellipsometric measurements on Bi-2212,154 with a transition at ~3.8 eV stronger and sharper for electric field polarized along the modulation direction. The ab-plane anisotropy has also been observed in the far-infrared transmittance of free standing Bi-2212 single crystals.155 Considering all of the above, we believe that the observed anisotropic behavior is an intrinsic property of these Bi-based cuprates. Optical conductivity

The Kramers-Kronig transformation of the polarized reflectance data of Bi(Pb)2212 yields the real part of the conductivity a1(w) shown in Fig. 28 for several temperatures. Essentially, the spectra are similar to Bi-2212.107"141 In all cases, as T is lowered from room temperate to just above Tc, we observe a sharpening and an increase of the far-infrared conductivity, on account of the increasing dc conductivity. At higher frequencies, a1(w) does not show much temperature-dependent variation.






91


In addition, the normal-state o1 (w) has a frequency dependence that decays much more slowly than the w-2 expected for a material having a Drude response. This non-Drude behavior, which is universal in the optical conductivity of the copper-oxide superconductors, has been the subject of considerable discussion and controversy.2-4

Upon entering into the superconducting state, the far-infrared conductivity falls rapidly to a value well below the normal-state value. The area (spectral weight) below T, is smaller than that above T,. The missing-area below T, is a effect of the condensation of the free carriers that are responsible for the normal-state transport into the superconducting pairs. The spectral weight under the o1(w) curve is removed from the finite frequencies and shifted into a 8 function at w = 0. The residual low-lying conductivity remains even at T < Tc. One possible origin of this is the low-frequency tail of the non-Drude component and other high frequency interband transitions. The other cause could be thermally excited quasiparticle infrared absorption associated with node(zeroes) of the gap function on the Fermi surface. There is also a kneelike structure developing in the superconducting state u1(w) at w ~ 500 cm-1. It was shown by Reedyk et al.33 that similar structure may occur due to interaction of an electron continuum with c axis LO phonons.33

As shown in Fig. 28, the anisotropy in the normal state conductivity is about 10%, with the far-infrared conductivity higher in the a direction and the high-frequency conductivity is higher along b. Below Tc there is a definite anisotropy to the farinfrared conductivity, with a considerably larger conductivity along the b axis down to - 20 meV. The anisotropic behavior of optical conductivity in Bi(Pb)-2212 is very similar to Bi-2212.107'141 However, there are important differences in the vibrational structures of o1(w) between the two materials. In Bi-2212,107'141 the phonon around ~ 630 cm-1 (not well screened by free carriers) is present for both polarizations at 300 K. In the b-axis spectrum, the phonon appears as two peaks, positioned near 630 and






92


655 cm-. The splitting of vibrational line at low temperature is probably due to the baxis superlattice structure. In Bi(Pb)-2212, the 640 cm-1 phonon mode is visible along the a and b axes, but stronger in the b direction in the whole measured temperature range, which led us to believe that Bi(Pb)-2212 is less structurally anisotropic. Thus, it is reasonable to speculate that the observed ab-plane anisotropy of Bi(Pb)-2212 is attributed to the anisotropy of electronic structure within the CuO2 plane, rather than the structural superlattice in the Bi-O layer. Oscillator strength sum rule

In view of the fact that the ab-plane anisotropic conductivity of Bi(Pb)-2212 shown in Fig. 28, it is important to quantify the spectral weight by integrating the optical conductivity from zero to a certain frequency hw. Based on the conductivity data, we define the partial sum rule, (m/m*)Nefi(w) as90



-]- Neff(w) = 2mVe - [11 (w' )dw', (12)
m ire2Nc, I
0

where m* is the effective mass of the carriers, m is the free-electron mass, Vce is the unit cell volume, and Ncu is the number of CuO layers per unit cell. Here, we use Nc. = 2 for Bi(Pb)-2212. (m/m*)Nff(w) is proportional to the number of carriers involved in optical excitations up to hw.

In Fig. 29 we plot the room-temperature results for (m/m*)Neff(W) per planar Cu atom along a and b axes. The inset shows the difference between (m/m*)Nef(w) for the two polarizations. First, (m/m*)Nr(w) shares a common feature along both directions: It rises rapidly at low frequencies due to a Drude-like band peaked at w = 0, and begins to level off near 8000 cm1, then rises again above the onset of the charge-transfer band. Second, the difference between (m/m*)Neff(w) for the two polarizations shows that there is more spectral weight (w < 5000 cm') in the




Full Text

PAGE 1

EFFECTS OF HIGH MAGNETIC FIELD AND SUBSTITUTIONAL DOPING ON OPTICAL PROPERTIES OF CUPRATE SUPERCONDUCTORS By HSIANG-LIN LIU A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF ^. DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1997

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ACKNOWLEDGMENTS It is my great plecisure to thank my supervisor, Professor David B. Tanner, for giving me the opportunity to be part of his reseaxch group and study a lot of very exciting projects detailed in this dissertation. His confidence and continued support are a very much valued contribution, as are the many suggestions and helpful discussions. He is also a good role model as a scientist and an educator. I will keep his attitude in mind: positive thinking, self-motivated, and enjoys working. I have been truly privileged to work with him. I would like to thank Professors P.J. Hirshfeld, J.M. Graybeal, D.H. Reitze, and J.R. Reynolds for reading this dissertation and for their interest in serving on my supervisory committee. Thanks also go to all my past and present colleagues in Tanner's group for their friendship, useful conversation and cooperation throughout my graduate work, M.A. Quijada, Y.-D. Yoon, A. Zibold, J.L. Musfeldt, K. Kamaras, U. Akito, A. Memon, CD. Porter, L. Tache, D. Stark, D. John, J. Laveigne, V. Boychev, and S.-K. Hong, I would like to acknowledge those who have generously supplied high-quality samples which were essential to the completion of this dissertation. They are Drs. M.Y. Li and M.K. Wu (Tsiang Hua University, Taiwan), M.J. Burns and K.A. Delin (California Institute of Technology) for studies of YBa2Cu307_5 films, Beom-Hoan 0 and J.T. Markert (University of Texas), G. Cao and J.E. Crow (National High Magnetic Field Laboratory) for studies YBa2Cu307_«-family single crystals, R.J. Kelly and M. Onellion (University of Wisconsin), H. Berger, G. Margaritondo, and L. Forro (Ecole ii

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Polytechnique Federale de Lausanne, Switzeland) for studies of Bi2Sr2CaCu208family single crystals, A.E. PuUen and J.R. Reynolds, L.-K. Chou and D.R. Talham (Department of Chemistry, University of Florida) for studies of organic conductors. In addition, I have greatly appreciated assistance from Dr. Y.J. Wang at the National High Magnetic Field Laboratory. I am also in the debt of Professor M.W. Meisel, Dr. J.S. Kim and T. Steve for the ac susceptibility measurements of organic conductors and highTc materials. I would like to thank Dr. K.A. Abboud for X-ray experiments of organic conductors. I theink the technical staff members in the physics department machine shop, electronic shop, and cryogenic for their efforts. I would also like to take this opportunity to thank my parents for their love cind support. Finally, but most importantly, very special and sincere thanks go to my wife Yu-Huei Chu, whose constant love, dedication, encouragement and guidance led me to the path and helped me to stay there. Financial support from the NSF (Grant No. DMR-9403894) is gratefully acknowledged. iii

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TABLE OF CONTENTS Page ACKNOWLEDGMENTS ii ABSTRACT vii CHAPTERS L INTRODUCTION 1 II. FAR-INFRARED PROPERTIES OF SUPERCONDUCTING YBa2Cu307-* FILMS IN ZERO AND HIGH MAGNETIC FIELDS 3 Introduction 3 Experimental 6 Results 9 Zero-field spectra 9 Magnetic field studies 10 Discussion 12 Dielectric function models 12 The vortex dynamics 15 Summary 21 HI. DOPING-INDUCED CHANGE OF OPTICAL PROPERTIES IN UNDERDOPED CUPRATE SUPERCONDUCTORS 37 Introduction 37 Experiment 39 Sample characteristics 39 Optical mecisurements 40 Results 4j Roomtemperature spectra 41 iv

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Temperature dependence in the infraxed 43 Discussion 44 Low-frequency spectral functions 44 Dielectric function models 46 Quasiparticle scattering rate 49 Superconducting response 54 Summary 61 IV. OPTICAL STUDY OF UNTWINNED (Bii.57Pbo.43)Sr2CaCu208+i SINGLE CRYSTAL: AB-PLANE ANISOTROPY 84 Introduction 84 Experimental 86 Results and Discussion 89 Polarized reflectance 89 Optical conductivity 90 Oscillator strength sum rule 92 Dielectric function models 93 Superconducting state 98 Summary 103 V. AB-PLANE OPTICAL SPECTRA OF IODINE-INTERCALATED Bii.9Pbo.iSr2CaCu208+«: NORMAL AND SUPERCONDUCTING PROPERTIES 113 Introduction 113 Experimental 115 Results and Discussion 115 Reflectance spectrum 116 Optical conductivity 117 Oscillator strength sum rule 120 Quasiparticle scattering rate 122 Spectral weight in the condensate 126 Summary 127 VL AB-PLANE OPTICAL PROPERTIES OF NI-DOPED Bi2Sr2CaCu208+« 137

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Introduction 137 Experimental Techniques and Data Analysis 138 Comparison of Ni-Doped to Pure Bi2Sr2CaCu208+5 140 Temperature Dependence of Ni-Doped 141 Reflectance spectrum 141 Conductivity and dielectric function 142 Two-component model 143 One-component analysis 147 Spectral weight 149 Superconducting-state properties 150 Simunaxy 152 VIII. CONCLUSIONS 165 APPENDICES A STRUCTURE AND PHYSICAL PROPERTIES OF A NEW 1:1 CATION-RADICAL SALT, C-(BEDT-TTF)PF6 169 B OPTICAL AND TRANSPORT STUDIED OF Ni(dmit)2 BASED ORGANIC CONDUCTORS 213 REFERENCES 249 BIOGRAPHICAL SKETCH 268 vi

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Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy EFFECTS OF HIGH MAGNETIC FIELD AND SUBSTITUTIONAL DOPING ON OPTICAL PROPERTIES OF CUPRATES SUPERCONDUCTORS By Hsiang-Lin Liu August 1997 Chairman: David B. Tanner Major Department: Physics Infrared and optical spectroscopies have been applied to study both the normal state and superconducting state electronic properties of cuprate superconductors. Two important parameters used in our experiments are the applied magnetic field and substitutional doping. Varying the magnetic field at constant temperature allows us to study the vortex d3mainics in the high-temperature superconductors. In contrast to several previous reports, we do not see any field-sensitive features in either far-infrared reflectance or transmittance spectra of YBa2Cu307_5 thin fihns at low temperatures. Only at fields and temperatures where the dc resistance is not zero-on accoimt of dissipative flux motion-there is a field-induced effect in far-infrared transmittance. We studied the a6-plane optical response of Y-doped Bi2Sr2CaCu208 and Prdoped YBa2Cu307_5 single crystals from underdoped to optimally doped regimes. It vii

PAGE 8

is difficult to relate our results of low-frequency spectral functions to the normal-state pseudogap. We have also found that there is a "universal correlation" between the numbers of carriers and the transition temperature. This correlation holds whether one considers the mmiber of carriers in the superfluid or the total number of carriers. The polarized spectra of Pb-doped Bi2Sr2CaCu208+i were also investigated. We find that although Pb doping removes the 6-axis superlattice structure, there is a definite a6-plane anisotropy of optical properties above and below Tc. Our results provide evidence that within the Cu02 plane the electronic structures of these Bibased cuprate superconductors are anisotropic, irrespective of the superstructure in the Bi-0 layer. In the iodine-intercalated Bi2Sr2CaCu208+« sample, we find that the infrared phonon spectrum and the visible-ultraviolet interband transitions axe modified after intercalation. The aft-plane optical conductivity results support the idea that interCcilated iodine increases the hole concentration in the Cu02 planes. The iodine is present as ions, most likely as Ij. Finally, the a&-plane optical spectra of Ni-doped Bi2Sr2CaCu208+5 were measured. We suggest that the low-frequency feature in the normal-state ai{(jj) is associated with the significant disorder induced by Ni impurities. In the superconducting state, a smaller superfluid density than implied by Tc from the Uemura line could be connected with the effect of impurity-induced disorder. viii

PAGE 9

CHAPTER I INTRODUCTION Eleven years have passed since the first cuprate superconductor Weis discovered. Although we have not yet reached a final goal of the elucidation of the high-Tc mechanism, a tremendous number of experimental techniques and theoretical work have revealed its electronic properties. Infrared and optical spectroscopies have played an important role in clarifying the electronic state of cuprate superconductors.^"* Infrared light probes the dynamics of the free carriers, the nature of chargetransfer and other low-energy excitations, the superconducting gap (in principle), phonons, and other aspects of the electronic structure. Because infrared penetrates a substcintial distance (~ 0.2-1 /xm) into the material, it is less sensitive than other probes (tunneling and photoemission, for example) to surface damage, especially if the surface layers are nonconducting. This dissertation is organized in such a way that each chapter is essentially selfcomplete and can be read without assuming special knowledge from another chapter. We present an experimental study of the infrared properties of highTc superconductors. The reflectance and/or treinsmittance of these materials has been meeisured at temperatures between 4.2 K and 300 K over wavelengths from the far-infrared (35 cm~^ or 4.5 meV) to the near ultraviolet (40000 cm~^ or 5 eV). Furthermore, two important parameters used in our measurements are the applied magnetic field and substitutional doping. Prom these experiments the optical conductivity, (Ti(u;), dielectric function, ei(u;), and other optical properties can be estimated. When a magnetic field is applied to the high-Tc superconductors, their mixed state properties are characterized by the existence of vortices. There has been con1

PAGE 10

2 siderable interest in vortex dynamics in the highTc materials, including their ac properties. In our work, we report the far-infrared reflectance and transmittance measurements of YBa2Cu307_i films. We use reflectance
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CHAPTER II FAR-INFRARED PROPERTIES OF SUPERCONDUCTING YBajCusOT-* FILMS IN ZERO AND HIGH MAGNETIC FIELDS Introduction The electronic properties of highTc superconductors are affected by the application of magnetic fields. The simple picture of the high-Tc materiads, in the mixed state, is the sample penetrated by an array of magnetic vortices each of which contains a quantized amount of magnetic flux. In the applied current density J*"^' and the average magnetic flux density B, there will be a Lorentz force density / = J*" x B on the vortices. If the vortices are at rest, the resistance will be effectively zero. If the vortices are moving with a mean velocity v, an electric field E = v x B appears and there is finite resistance. However, the behavior of the complex dynamics of vortex motions in the presence of viscous, pinning forces, and fluctuations either of thermal origin or due to the influence of defects in the sample becomes complicated and is not yet well understood. Indeed there have been controversies regarding the ac properties of the vortices in the high-Tc superconductors. In spite of the challenges, there is growing interest in vortex state electrodynamics on the high-Tc superconductors over a broad range of frequencies.^"^ Historically, microwave experiments have been widely used to study the vortex dynamics in type II superconductors.^ When the vortices are pinned, their dynamics are invisible to dc transport. On the other hand, microwave measurements can sense the fluctuations about the pinning sites. Measiuring the complex surface impedance provides information related to the effective pinning force constant and vortex viscosity. There were 3

PAGE 12

4 already numerous measurements on the eflFect of magnetic field on the microwave response functions of the high-Tc superconductors. ^"^^ It is generally agreed that the microwave results are affected by two mechanisms: vortex motion and superconducting condensate depletion. More recently, teraJiertz time domain spectroscopy spans the frequency from 100 to 1000 GHz (3.3-33.3 cm-^).^^-^^ The nonlinear dependence of the complex conductivity as a fimction of magnetic field has been interpreted in terms of enhanced pair breaking due to nodes in the gap function. At higher frequencies, fax-infrared spectroscopy has been applied to investigate the vortex dyn«imics in the highTc superconductors. During the past several years, the far-infrared properties of the highTc superconductors in zero magnetic field have been extensively studied in an effort to understand the mechanism of high-temperature superconductivity.* More recent interest has concentrated on the change in the far-infrared response in an applied magnetic field. In most cases, evidence for additional absorption is seen. Still, there are some contradictions among these measurements. The early report by Brunei et al}^ on the reflectance ^ measurements of Bi2Sr2CaCu208 (BSCCO) at several far-infrared frequencies a; as a function of temperature T and magnetic field up to 17 Tesla, has inferred a value for the superconducting gap by setting 2A{T,H) = hu at the T and H where ^ first drops below the low-T, zevo-H value. In their data, the drop in farinfrared reflectance corresponds to the onset of the resistive state and thus only occurs at the higher temperatures or fields. In contrast, the far-infrared transmittance measurements through a thin film of YBa2Cu307_i (YBCO) in a strong magnetic field by Karrai et al}"^^^^ show an increase in transmission below ~ 125 cm~^ with increasing field. This is attributed to the dipole transitions associated with bound states in the vortex cores. Evidence for magneto-optical activity was also found, interpreted as cyclotron resonance in the mixed state. These effects occurred at temperature as low

PAGE 13

5 as 2.2 K and in magnetic fields up to 15 Tesla. Later, several theoretical calculations of the optical response of the vortex core states have been published.^^"'^^ The theory of Hsu including the vortex motion^^'^^ describes the experimentally chiral response^* very well, but the agreement for the nonchiral response at ~ 65 cm~^,^^ which the authors attributed to the vortex core resonance, is only partial. Shimamoto et al}^ observed the general trend of far-infrared transmission to increase on both YBCO and Bi2Sr2Ca2Cu30i films with fields to 100 Tesla. The field-induced transmission change abruptly increases at around Tc with decreasing temperature and tends to saturate to a constant at temperature down to 10 K. The authors explained this feature by a flux low model. Gerrits et al.^^ reported practically no influence of the magnetic field up to 15.5 Tesla on the far-infrared reflectance measurements of YBCO thin films at 1.2 K. Eldridge et al}^ meaisured the ratio of normal incidence reflectance ^ of a YBCO film in a magnetic field to that in no field, in conjimction with a separate measurement of .^(0), to obtain the absolute values of ^{H= 0.7, 1.4, and 3.5 Tesla) at 4.2 K. A Kramers-Kronig analysis then gave the field-dependent conductivity which shows a broad resonance between 50 and 250 cm~^. They eire able to fit the shapes, but not the magnitude, of the peak by the theory involving vortex motion with pinning. In this chapter, we report the farinfrared reflectance {^) and transmittance measurements of YBCO films at temperatures between 4.2 and 300 K and in magnetic fields up to 30 Tesla. This work is diff^erent from earlier spectroscopic studies, as we use ^ and ^ to extract frequency-dependent optical conductivity as a function of temperature and applied magnetic field. Comparison of temperature-dependent results with previous published data'^^-'^'^ achieves a consistent description of the twocomponent dielectric response, with the free carrier component condensing to form the superfluid below Tc. However, as varying the magnetic field (with H perpendicular to

PAGE 14

6 the ab plane ajid with unpolaxized light) at constant temperature as low as 4.2 K, the conductivity spectrum shows no discernible field dependence. This observation differs from several previous fax-infrared measurements in this temperature rajige. Only at fields and temperatures where the dc resistance is not zero-on account of dissipative flux motion-is there a field-induced effect in infrared transmit tance. Experimental We have studied three types of YBCO films. Type one of samples weis made by a KrF excimer laser (wavelength of 248 nm) on YAIO3 substrates at Jet Propulsion Laboratory. The YAIO3 substrates were 0.25-mm-thick, (OOl)-oriented and doped with 20% Nd on Y sites to suppress twinning. The nominal growth process is done in the following way. The substrates are mounted on Haynes alloy plates using Ag paint. These axe transferred into the deposition system via a load-lock. Those substrates axe buffered using a 200A PrBa2Cu307_5 (PBCO) layer deposited by pulsed laser deposition at 790°C, 400 mTorr of O2, at a fluence of 1.6 J/cm^. Substrates are heated radiatively and monitored by a thermocouple that is cross-checked by an optical pyrometer prior to film growth. The PBCO layer is followed by a YBCO layer deposited at 810°C, 200 mTorr of O2, and 1.6 J/cm^. The deposited bilayer is cooled in situ at 40°/minute in a 500-650 Torr O2 atmosphere from the growth temperature down to room temperature. The film thickness is typically d = 300 ~ 500A. The second type of samples was also prepared by pulsed-laser ablation at Tsing Hua University. The films (d = 400 ~ 6OOA) were grown on 0.5-mm-thick, (OOl)-oriented MgO substrates. The laser energy for YBCO target is about 1.5 J/cm^. During the deposition, the oxygen pressure and substrate temperature are 400 mTorr and TSO^C, respectively. The film is cooled in situ in one atmosphere O2 to ~ 500° over an hour period, and then followed by slow-cooling to room temperature. The third sample is 5000-A-thick film deposited on a SrTiOa substrate by the similar method.

PAGE 15

7 All the samples have been structvirally characterized by x-ray diffraction, which has clearly shown their c-axis orientation. The superconducting properties of films have been determined by dc resistivity or ac susceptibility measurements. The characteristics of all samples axe listed in Table 1. Figure 1 illustrates the temperaturedependent dc resistivity data. The 5000-A-thick film gives a slight higher onset temperature and shcirper transition width. On the other hand, samples prepcured in similai conditions have shown close values of resistivity at room temperature. Table 1. Sample characteristics. Sample Tc ATc (Tdc{a.t 300 K) K K n ^cm 300A YBCO/2OOA PBCO/YAIO3 83.5 3.5 1820 500A YBCO/200A PBCO/YA103 85.0 2.5 1700 400 A YBCO/MgO 83.0 3.0 2500 600 A YBCO/MgO 86.7 2.8 2800 5000 A YBCO/SrTiOs 88.0 0.5 3100 All thin films have been studied in reflectance {^) and transmittance (^, whereas the 5000-A-thick film on SrTiOa has been studied by ^. Temperaturedependent (10-300 K) ^ and at zero magnetic field were performed from 35 to 600 cm~^ using a Bruker 113V Fourier transform spectrometer equipped with a constant flow helium cryostat. Far-infrared studies in a magnetic field have been carried at the National High Magnetic Field Laboratory. Our measurements used a Bruker spectrometer and light-pipe optics to carry the far-infrared radiation through the magnet. The sample probes in conjimction with a 20-Tesla superconducting magnet are designed to enable alternate sample and reference measurements (for both ^ and

PAGE 16

8 ST)^ eliminating instabilities of the spectrometer. For the reflectance data, cin Au mirror has been used as a reference, while the trcinsmittance wais done relative to ein empty diaphragm. The absolute values of the overall ^ and ^ in the sample are obtained at 4.2 K and applied fields up to 17.5 Tesla. We also employed a 30-Tesla resistive magnet to study the magnetic field effects. Note that in this configiuation, only the transmittance ratio is accessible. Thus, we report \^{JtV) / ^(0)] at the constant temperature running over a range between 4.2 cind 100 K. In all measurements, the unpolarized far-infrared radiation was incident nearly normal to the film , so that the electric field Wcis in the ah plane. The magnetic field H was perpendicular to the ah plane. A detailed description of the experimental setup is given elsewhere."^* The complex dielectric function e(u;) or optical conductivity (a>) j directly calculated from the measured SI and in the far-infrared region. To deal with dispersive and absorption effects in the substrate, the reflectance St sub and transmittance .^gub of a bare YAIO3 and MgO were also measured at each temperature and magnetic field where the film data were taken. The absorption coefficient a(w) and the index refraction n(u;) of the substrate were then used in analysis of the data for the films. In this case, we found for the calculated dielectric response at low frequencies (u; < 100 cm~^) is compjirable to those obtained by optical reflectance of bulk, single crystal, and thick-film samples followed by KramersKronig analysis where extrapolation to zero and infinite frequencies were needed. A detailed discussion of the analysis for transmittfince and reflectance data has been given in previous work.'^^''^^

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9 Results Zero-field spectra The zero-field fax-infrared reflectance and transmittance of 500A YBCO/200A PBCO/YAIO3 and 400 A YBCO/MgO films at six temperatures below and above Tc are shown in Fig. 2. Measurements on 300 A YBCO/200A PBCO/YAIO3 and 6OOA YBCO/MgO films revealed similar results. We have found small transmitted intensity < 15%) for different films, where generally much of the behavior over 100-600 cm~^ is due to phonon processes in the YAIO3 and MgO substrates. Despite the fact that the far-infraxed spectra are complicated by the substrates, one can clearly observe the intrinsic response of the YBCO films in the data. Below Tc, superconducting films strongly screen the applied electromagnetic field giving the low-frequency reflectance close to imity, while the transmittance tends to zero. A finite treinsmittance at w = 0 corresponds to a finite dc conductivity. Our zero-field spectrum of a 400 A YBCO/MgO film is compatible with that on a 480A YBCO/MgO film reported previously by Gao et al.^^'^^ We extracted the real and imaginary parts of the conductivity directly from the experimental reflectance asid transmittance of the films. In the following, we concentrate the behavior on the far-infrared region below 150 cm~^ for the YBCO film on the YAIO3 substrate and 300 cm for the YBCO film on the MgO substrate since both substrates are mainly opaque above these frequencies at all temperatures.^^ The upper panels of Fig. 3 (a)-(b) show the real part of the conductivity cri(a;). In the normal state, (Ti(a;) approaches the ordinary dc conductivity. In the superconducting state, the spectral weight loss can be seen for T < 80 K, implying a shift of weight to the origin. Focusing on the data below 100 cm~\ we observe that
PAGE 18

10 the model analysis of the data. At T 0) reaches a value of about 6000 cm~^. This is approximately two times larger than the Kramers-Kronig results seen in the a-axis conductivity of YBCO single crystals, ^'^'^^ but coincides with those previous data by microwave techniques.^^ The imaginary part 0-2(0;) is plotted in the lower p«inels of Fig. 3 (a)-(b). When T dependence for u; < 100 cm~\ consistent with the behavior of London electrodynamics. In contrast, (72(0;) falls off more slowly than l/ui at higher frequencies, on account of both the broad mid-infrared contribution and a remaining normal Drude component. We also notice that at low frequencies, 0-2(0;) > 0-1(0;), indicating the inductive current dominates over the conduction current in the superconducting state. When the temperature is increasing, 0-2(0;) decreases monotonically and changes the slope at the superconducting transition. Above Tc (T = 100 K), 0-2(0;) extrapolates to the origin, as expected for a normal metal. To this end, it is important to point out that the optical conductivity o-(a;) = (o;/47r)Im[c(u;)— 1] can be well fitted by the model discussed later. Magnetic field studies In Fig. 4 we show the reflectance and transmittance of a 500A YBCO/200A PBCO/YAIO3 film taken at 4.2 K and at several magnetic fields. We observed practically no influence of the magnetic field on the infrared reflectance of the film . Moreover, the field-dependent features in the transmittance spectra axe due to impurity effects in the YAIO3 substrate. The magnetic field and frequency-dependent conductivity of this film are shown in Fig. 5. The spectra show no discernible field dependence at 4.2 K. This observation differs from pre'\aous far-infrared measurements in this temperature and frequency range. ^'^•^^'^^ Despite the lack of field dependence in the either ai or 0-2 spectra, two interesting observations can be made. First, with the external field perpendicular to the ab plane of the superconducting YBCO film,

PAGE 19

11 no far-infraxed magnetoresistance was detected at 4.2 K and in the high-field regime. Second, down to the low-frequency limit (~ 35 cm~^) of our measurements, the dielectric response does not change with magnetic field. Our results differ from the data obtained in the terahertz studies which reported the change in the ai and 0. Upon increasing frequency it falls off slowly, with a pronounced shoulder at ~ 450 cm~^ On the other hemd, the lower panel of Fig. 6 displays the fax-infrared reflectance of the film at 4.2 K as a function of magnetic field. We find no field-induced effects in the spectra. In particular, the field independence of the 450 cm~^ edge favors the non-superconducting explanations of this feature. It is generally accepted that this structure is due to interaction of an electron continuum with LO phonons along the c axis.^^ Again, our results are in agreement with one earlier experiment,"^* but in contrast to several previous reports. ^^'^^'"^^ To investigate further, the magneto-transmission measurements taken at several temperatures and magnetic fields for both 400A and 600A YBCO/MgO films are shown in Fig. 7, 8 (a) (d), respectively. The data were obtained by taking the ratio of the transmission of the sample at H to the zero-field transmission. It is cleai that the ratio for the 400A film did not show any discernible field dependence at 4.2 and 50 K with fields to 27 Tesla. Similarly, we do not find any evidence for changes in the transmission ratio for the 600A film in this temperature and field range. Here it is necessary to point out that typical noise variations of our measurements in a magnetic field eire on the order of ± 1%. On the other hand, we are imable to pursue our studies at lower frequency (a; < 35 cm~^) on these films due to the low transmitted intensity (progressively deteriorating signal to noise ratio) in the superconducting state. When

PAGE 20

12 the temperature is raised above 60 K, at 35 cm~^ the transmission of these fihns is seen to change by more than 5% with increasing fields from 6 to 27 Tesla, while the changes at higher frequencies (w > 100 cm~^) axe not well resolved within our experimental error. It should be noted that the Icirge magnetic field induced increase in transmission at low frequencies occurs at a temperature not too far below Tc. In contrast, the spectra change sign at 95 K for the 400A film, and there is a decrease of the transmission with applied field. Discussion Dielectric function models In this section we turn to an analysis of the conductivity as obtained from the reflectance and transmittance data. We first consider the temperature-dependent spectra of the films in the normal state at zero field. There has been much discussion over the two-component and the one-component pictures to describe the optical conductivity of highTc superconductors."* Two-component model views the conductivity as two sets of charge carriers comprising of both a Drude contribution centered at u = 0 and a secondary mid-infrared absorption band arising from bound chcirges such as interband transitions. One-component model assumes a single carrier with a frequency dependent scattering rate due to coupling between the carriers and optically inactive excitation, such as spin excitations. Because the data extend only to 150 cm~^ in the 500A YBCO/2OOA PBCO/YAIO3 film, we found that the Drude model Ccin describe the optical conductivity well. In the case of the 400 A YBCO/MgO fibn up to 300 cm~\ it seems necessary to allow for a second component in addition to the simple Drude one. The dielectric fimction is written as

PAGE 21

13 where the first term represents the Drude component described by a plasma frequency ijjpD and scattering rate l/r/j; the second term is a Lorentz oscillator to represent one additional absorption bcind which is at frequency We? has oscillator strength Wpe, and width 7e. The last term, e,>, is the high frequency limit of e(u;), which includes higher frequency interband transitions. In the superconducting state, a two-fluid analysis is used. Here, it is assumed that a fraction of the carriers (the thermally excited quasiparticles) display normal Drude behavior whereas the remaining part condenses to form a 8 ftmction at u; = 0. The dielectric function is expressed as (^«r> ^^no where u)ps represents the oscillator strength of the superconducting condensate, tO''" is the scattering rate of the S function at T < TcThe quantity u}^g+u)p„ = J^jj gives the total numbers of carriers in the two-fluid model. A consistent and independent check of the fitting procedure is to compute the real and imaginary parts of the conductivity of the film with the parameters that we have obtained by fitting the experimental transmittance data. We then recall the reflectance data and their Kramers-Kronig form using the crj and (T2. It is found that the experimentally measured single boimce reflection of the substrate [il, « (^^) ] agrees with the calculated reflectance spectra. Figure 9 (a) shows the experimental (symbols) and fitted (solid lines) conductivity spectra of a 500A YBCO/200A PBCO/YAIO3 film at 20, 100, and 300 K. We fixed e,> = 25 and varied the two-fluid parameter and ujpn as well as the quasiparticle scattering rate l/r/j. It turns out that the models give reasonably good fits to the experimental data both in the normal and superconducting state. The Drude plasma frequency, u)pj) = 7100 ± 100 cm~\ is essentially temperature independent.

PAGE 22

14 We also found that the value of superconducting plasma frequency a>p5, obtained from the above analysis, is about 6000 ± 100 cm~^ at 20 K. The superfluid density fraction [fs{20 K) = ^^5(20 K)/u;2^] is estimated to be 71%. The inset of Fig. 9 (a) displays the temperature-dependent scattering rate I/tj) from the free-carrier or Drude contributions. It appeaxs that 1/tq has a linear temperature dependence for T > Tc, wherecis below Tc the two-fluid model gave a rather sudden drop in 1/td with saturation at T < 50 K. In the normal state, the linear 1 /tq is a unique property of the copper-oxide superconductors and reflects the dc resistivity data. Writing h/rj) = 2xA/j ksT + h/TQ, \d is the dimensionless coupling constant that couples the charge carriers to the temperature-dependent excitations responsible for the scattering. In addition, the zero temperature value I/tq is assumed to result from elastic scattering by impurities. We can obtain the coupling constant and intercept, from the straight line fit, as A/) ~ 0.23 and I/tq ~ 80 cm~^, As was stated previously, the temperature-dependent cr\{T) at low frequencies exhibits a peaJc below Tc. The physical origin of this behavior has been discussed previously.^^'^^'^^ The peak in a\ is attributed to the rapid drop in the quasipaxticle scattering rate combined with a more slowly decreasing normal-fluid density. In the case of the 400 A YBCO/MgO film, we found that we could obtain good fits by adding one more oscillator, Ue = 10000 cm~\ uipe = 206 cm~^ and 7e = 600 cm~^ Because the Icirge lattice mismatch exists between the YBCO film and MgO substrate, defects or disorder in the interface layer might be responsible for this absorption band. Fitted conductivity spectra are shown in Fig. 9 (b). The parameters that fit the spectra are the Drude plasma frequency ujpD = 8500 ± 100 cm~^ cind the superconducting plasma frequency UpS = 7000 ± 100 cm~^ at 10 K. The fraction of superfluid condensate is about 68% at T < Tc. Our results are similar to the previous work on the analysis of a 480A YBCO/MgO film by Gao et a/.^^-^^ in addition, the

PAGE 23

15 inset of Fig. 9 (b) shows the normal-state 1/t£) is lineax in temperature; it decreases quickly below TcI/tjj from the inelastic and elastic scattering processes gives the values of A ~ 0.20 and I/tq ~ 66 cm~\ respectively. Taking the Fermi velocity to be Vf = 1.4 X 10^ cm/sec^® and using the scattering rate of 1/t£)(100 K) = 180 ~ 200 cm~^ for the above two films, we can estimate the mean free path (/ = vf r) about 40 A. This evidence (/ > , where the superconducting coherence length ( is about lO-lsA in the cuprates) added to the small value of Xjy indeed suggest that our films axe clean-limit and weak-coupling superconductors. Concerning the superconducting fraction /s(T'), this quantity is essentially a measure of the strength of the S function in (Ti{u) and is related to the superconducting penetration depth A^. In Fig. 10 we plot the frequencydependent penetration depth Ai(a;), defined as Xi{uj) = ^ (? j^.'Kuaiiyj) where c is the light speed, for our YBCO films at T TcThe fact that A/, (a;) shows some frequency dependence below 150 cm~^ is an indication that not all of the free carriers have condensed into the S fimction. The penetration depth can be converted to the plasma frequency of the condensate, A^ = cjuj^sThe extrapolated zero-frequency value Ai(u; 0) is fo\md to be 2600 ± 100 A and 2400 ± 100 A for 500A YBCO/200A PBCO MgO and 400A YBCO/MgO; this gives Wp, = 6000 ± 200 cm"^ and 6600 ± 200 cm-\ respectively. We note that the translation of the superfluid oscillator strength from Ai(0) is close to the fitting value in the two-fluid model. Also, it is worth mentioning that the penetration depth for our films is larger than 1600 ~ I8OOA reported by infrared reflectance measurements of bulk YBCO single crystals^^ and thick YBCO films.^'^ Two possibilities for this discrepancy can be made. First, there is incomplete condensation in our films; the smaller superfluid density yields the larger penetration depth. Second, the experimental imcertainty in the film thickness would affect the absolute Vcdue of the penetration depth.

PAGE 24

16 The vortex dynamics In the presence of a magnetic field the electrodynamic response of type-II superconductors is aifected by vortex dynamics. We first discuss the magneto-optics data at our lowest temperature at 4.2 K shown in Fig. 4, 5, 6, 7, 8. Surprisingly, our spectra do not show any change with applied field, which is in agreement with one early work,'^'* but in contrast to several previous reports. ^^'^^'^^'^^ To acquire a better understanding, we consider the simple picture at T Tci The vortex can be driven either by an ac electric field or by superflow. Due to our high-frequency field oriented parallel to the ab plane, the vortices oscillate within their pinning potential.^* Demircan et al.^^ have implied the natural motion of the vortices in superfluid is of cyclotron type, i.e., adiabatically follows the superconducting condensate. In this case we have nondissipative vortex flow. The area of the vortex cores is in the normal state and the outside of them is in the superconducting state. The fraction area of the cores is H/Hc2{T) and Hc2 is upper critical field. The dielectric function of this system at low temperatures may be written as ^ ^ u{uj + iO+y Hc2^ u{uj + i/TsyHc2^ u;{u + i/TD) ul-uj^-iu^e (3) Here, l/r^ is the damping constant inside the vortex. The entire change in the dielectric response will be attributed to the pair-breaking effect and the quasiparticle excitations inside the vortex cores. Indeed, the depletion of the superfluid condensate has been seen in YBCO and BSCCO films using terahertz impedance measurements. ^^^^ In their data, the field dependence of the observed magnetoresist
PAGE 25

17 i.e., cr{u}) = (Ta(a;) + (Tni^^), where 0-3(0)) = 71,6^/1771*0; and cr„(o;) = (n„e'^/m*)S{a;). S(o;) is the frequency dependence of the quasipaxticle conductivity and initially dominated by the term of l/[(l/r£) iu)]. The change in cr(o>) due to a conversion of super to normal fluid is given by Acr(o;) = o;p£>A(n„/7i)[5(w) — i/u>]. Specifically, A) is maximum at zero frequency and decreases rapidly with frequency for (otq >^ 1. In our present work, the experiments are limited to o; > 35 cm~^ and the quasiparticle scattering rate 1/tj) of our films is smaller than 50 cm~^ for T < 50K at zero field, shown in the inset of Fig. 10. Moreover, the change in A<7(o;) is expected to be not big for fields up to our maximum field of 30 Tesla when Hc2 is greater than 100 Tesla. Thus, it is possible to say that any change of the spectra should be relatively small in our far-infrared frequency and high-field range. Further study at very fax-infrared frequencies is clearly needed to probe the effect of field-induced pair-brealcing. Meiny studies have focused on the quasiparticle local density of states inside a vortex core."*""^^ The physics of the vortex core for a type II superconductor is usually described by the Bardeen-Stephen model.^^ This model is based on the dirty limit description {I < which the motion of the quasiparticles gets well randomized within the core. The first calculations of the electronic vortex structure in the clean limit (/ > 0 and for H < Hc2 were performed by Caroli et 0/.^°''*^ Subsequently, Kramer and Pesch^^'^"* discussed the spatial structure of a vortex in a type-II superconductor in the clean limit and for 5-wave symmetry of the order parameter. They showed the radius of a vortex core decreases proportionally to T with decreasing temperature. An important point underlying this peculiar behavior, namely the change of the core size as temperature is lowered, is the existence of a quasicontinuum of the bound states in the vortex core. In the quasiclassical limit we have (kp ^ 1 and the energy of the lowest bound state (minigap) A^/Ef oc is very small. This picture is well established in the classical superconductors. However, for the high-Tc super-

PAGE 26

18 conductors the situation is quite different, since A is larger and Ep is smaller than in the classical superconductors, {(^ is by about four orders of magnitude smaller than in classical superconductors). Hence, only a few bound states in the vortex core are expected for the highTc superconductors. Recent spectroscopic experiments appear to have confirmed this expectation. ^^'^'^ A characteristic resoueince has been observed by Karrai et al}"^ in the mixed state of YBCO thin films at ~ 65 cm~^ They interpret their spectra as the vortex core resonance frequency. Bcised on the microscopic theory of vortex dynamic developed by Hsu,^^'^° this feature corresponding core level spacing ^flo = £'1/2 ~ ^-1/2 is about 40 cm~^ (~ 5 meV). Evidence for a laxge core spacing has also found in scanning tunneling spectroscopy (STS) on YBCO single crystals. In contrast, such dipole transition between the quasipaxticle levels in the vortex core is not present in our high-field measurements. In view of these differences, we suggest that anisotropic pairing (or gap) effect in the high-temperature superconductors might lead to the complexity of excitations inside a vortex core. We note that for the case of d-wave superconductors the quasipaxticle levels in the vortex core have a number of significant differences from the 5-wave case. In addition to the set of localized levels similar to that found in s-wave superconductors there are also continuum levels outside the core that axe associated with 3-wave admixture induced by the vortex.^^~^° Kopnin and Volovik^^ pointed out in a clean d-vr&ve superconductor, the electronic density of states induced by a vortex actually exhibits a divergency at low energies: iVvortex{^) l/\E\. It is a result of gap nodes in the excitation spectrum outside the vortex core. 1/\E\ divergence will presumably be cut off in a dirty rf-wave case. At a higher field, the distance between the cores becomes small; the electronic structure of the vortex core must be influenced by the competition between electrodynamic effects and spaticd variations of the superconducting order parameter near the vortex core. Thus, it seems likely

PAGE 27

19 that the excitations from the continuum levels might obscure the contribution of the ^±1/2 state. Another possibility is that the oscillator strength of the J5±i/2 state was too small to be seen in our present data. Furthermore, the STS experiments demonstrated very few quasipaxticle states can exist inside an YBCO vortex core and vortex cores axe in an extreme quantum limit. For our YBCO films, we may approach already this quantum limit, where the core region of the vortex is empty of the low-energy excitations. As is described previously, for frequencies below 200 cm~^, Karrai et al}^ also reported the chiral resonance on thin films of YBCO which the system exhibits free hole-like optical activity. Recently, several new chiral effects have been observed: the vortex pinning resonance,^'^ grain-boundaxy-induced vortex core excitations,^^ and hybridization of the cyclotron and vortex core resonances with the pinning resonance.^^ The chiral response will be a subject for further investigation in our future work. We will now discuss the high-temperature magneto-transmission data. As can be seen in Fig. 7, 8 (a)-(d), the contrast between the high and low temperature data is striking. Above 60 K where the system enters the flux flow regime, we observed the field-induced increase in transmission at low frequencies. We note that at these elevated temperatures one may expect that vortices become more mobile and thermally cictivated (Brownian) motion becomes possible. The electromagnetic interaction of the induced currents with the vortex lattice due to the Lorentz force was treated explicitly in the early work of Bardeen and Stephen,^^ and more recently by Brandt, Coffey and Clem,^^ and Tachiki et al.^"^ In these models, the interaction with the vortices is treated phenomenologically by introducing an effective pinning force constant Kp, vortex viscosity rj, and vortex mass M. Therefore, the dielectric function which includes the contribution from the vortex motion is given by

PAGE 28

20 ^^'^^ cj^ Hc2{'^-i^Tv Mu^lKp) u}{u} + i/T[)) u;2 u;2 turye (4) where = T]/Kp is the relaxation time of the vortex motion. Unfortimately, it is difficult to relate our experimental data to the above model because the case of a clean limit in our films must be distinguished from the Bardeen-Stephen*^ model which is valid in the dirty limit. Furthermore, we are presently imaware of any calculations for the vortex dynamics in the flux flow regime taking into account the influence of a clean limit and possibly anisotropic symmetry of the order parameter. A feeling for an enhancement of the transmission with magnetic field may also be obtained in the following way. The total transmittance through a thin film of thickness c?
PAGE 29

21 vortex liquid states) on the H-T phase diagram. At low temperatures the vortices are not easily moved due to pinning effects, i.e., vortex lattice is most likely a solid and the magnetic field has no effect on the spectra. However, when temperature is increased into the vortex liquid state and the flux pinning is overcome, vortex motion is driven by optical current and there is a corresponding change in the far-infr«ired properties. Thus, a magnetic-field-induced enhancement of the transmittance can be explained as a flux-flow phenomenon. Summary In sunmiarj', we have presented the temperature and magnetic field dependence of the far-infrared optical data on YBCO films where both the reflectance and transmittance have been measured. At zero field, we emphasized the two-component picture analysis for both the normal and superconducting states. The Drude plcisma frequency is essentially temperature independent, wherccis the scattering rate heis linear temperature dependence in the normal state followed by a fast drop below Tc. A weakcoupling strength A£> ~ 0.20-0.23 is derived. The superconducting condensate carries most (~ 70%) of the free-carrier oscillator strength, evidence for the clean-limit in our films. Varying the magnetic field at constant temperature allows us to study the vortex dynamics in the high-temperature superconductors. In contrast to several previous reports, we do not see any field-sensitive features in either far-infrared reflectance or transmittance spectra of YBCO films at temperature as low as 4.2 K. This observation suggests the following points: (1) The pairbreaking effects could be too small to be seen in our frequency and field range. (2) The anisotropic pairing (or gap) effects in the high-temperature superconductors might lead to the complexity of excitations inside a vortex core. The contrast between the high and low temperature data is striking. At a temperature not too far below their transition temperature, we observed

PAGE 30

22 the field-induced increase in transmission at low frequencies, which can be explained as a flux flow resistance. It is unclear why this effect changes sign above Tc and shows a decrease of transmission with applied field. Though there are still a lot of controversies on the experimental data and even more on their interpretations about the far-infrared optical studies regarding the vortex dynamics, we hope that our preliminary results will stimulate more completely and rigorously experimental and theoretical work for understanding the electrodynamics of cuprates in a magnetic field.

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23 1 .0 I — I — I — I — I — I — 1 — ' — I — I — I — I — I — I — ' — I — ' — ' — ' — ' — I — ' — ' — ' — ' — i — ' — ' — ' — ^ YBa2Cu307_5 films 300X YBCO/2OOA PBCO/YAIO3 500X YBCO/200X PBCO/YA1O3 4OOA YBCO/MgO 6OOA YBCO/MgO 5OOOA YBC0/SrTi03 0.6 0.4 0.2 I Q 1 I I I I I I iiij I I I I I I I I I i I I I I I i I I I I 0 50 100 150 200 250 300 Temperature (K) Fig. 1 The dc resistivity in the ab plane, as a function of temperature, for the YBCO fihns.

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24 Photon Energy (meV) 20 40 60 o o u ^— 01 0 U c o 1 .0 0.8 0.6 0.4 0.2 0.0 0.20 0.1 5 -I — I — i — I — I — I — I — I — I — I — I — I — r "1 — I — 1 — I — I — I — rI I I I I I I I I I I I I I (a) 500A YBCO/2OOA PBC0/YAI03_ c 0.1 0 o 0.05 \ \ \ 20 K 50 K 75 K 100 K 200 K 300 K 0.00 J I L I -J — I — I — I 1 I I 100 200 300 400 500 Frequency (cm~^) 600 Fig. 2 The measured fax-infraxed reflectance (upper) and transmittance (lower) of (a) a 500 A YBCO/200A PBCO/YAIO3 and (b) a 400A YBCO/MgO films at six temperatures and at zero field.

PAGE 33

25 Photon Energy (meV) 20 40 60 1 .0 0.8 (D O C 0.6 O o a: OA 0.2 0.0 -1 — I — 1 — I — I — I — I — I — \ — 1 — I — I — I — I — I — I — r -1 — I — I — I — I — I — r H — I — I — i — — I — I — hH — — I — hH — I — — h I I I I I I I I (b) 400A YBCO/MgO _ 600 Frequency (cm ) Fig. 2-continued

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26 Photon Energy (meV) 0 10 0 10 0 10 0 10 0 10 0 10 1 0000 1 1 1 1 1 0 50 100 0 50 100 0 50 100 0 50 100 0 50 100 0 50 100 150 Frequency (cnn~') Fig. 3 The real and imaginary parts of the optical conductivity extra<:ted from the experimental reflectance and transmittance of (a) a 500A YBCO/2OOA PBCO/YAIO3 and (b) a 400A YBCO/MgO films. The symbols show the dc values.

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27 Photon Energy (meV) 0 20 0 20 0 20 0 20 0 20 10000 8000 6000 4000 2000 -(b)' _ 10 K n M 1 M 1 1 1 1 1 1 1 1 1 1 1 _ 50 K 1 1 1 1 1 1 1 M 1 1 1 1 1 1 1 1 1 -s^70 K 1 M 1 1 1 1 1 1 1 1 1 1 1 1 M 1 _ 100 K _ TrrrF 1 1 r 1 1 r 1 1 r r 1 1 1 _ 150 K _ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 i 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 !] 1 1 1 1 1 1 1 1 1 1 1 1 L 10 K 25000 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 20000 15000 10000 5000 0 ' ' ' I I I ' I ' 1 ' ' 1 I I I I 1 I I I I I M I I TT T I 1 I T r 1 1 1 TTT TT T T I I r 1 1 j r r I I 50 K I 70 K I 100 K _ I I I I I ' I I 1 I 1 I 1 I 1 I I ' I I I ' ' ' I I I 1 I I I I 1 I I I I I 150 K _ 0 100 200 0 100 200 0 100 200 0 100 200 0 100 200 300 Frequency (cm"') Fig. 3-continued

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28 Photon Energy (nneV) 10 20 30 1.05 0.95 o c o "u 0.85 0) 0.75 -1 — I — ! — I — r-1 — I — I — I — I — I — I — I — I — I — I — I — I — I — I — I — I — I — P — I — I — I — I — 1 — n 0 Tesia 3 TesIa 5 TesIa . 12 TesIa 17.5 TesIa 0.65 H — I — I — M — — I — — I — \ — h I I I I 0) O C 0.10 o V) P 0.05 0.00 500A YBCO/2OOA PBCO/YAIO3 T = 4.2 K 0 TesIa 6 TesIa 12 TesIa 1 7.5 TesIa -J I I L. 50 100 150 200 250 Frequency (cm~^) 300 Fig. 4 The 4.2-K reflectance (upper) and transmittance (lower) of a 500A YBCO/2OOA PBCO/YAIO3 film at several magnetic fields.

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29 8000 Photon Energy (meV) 5 10 15 -I 1 r6000 I E o 0 Tesia 6 TesIa 12 TesIa 17.5 TesIa G 4000 2000 20000 ^ 15000 G 500A YBCO/200A PBCO/YAIO. T = 4.2 K 0 TesIa 6 TesIa 12 TesIa 17.5 Telsa 1 0000 b 5000 ° 50 100 150 Frequency (cm~^) Fig. 5 The magnetic field and frequency-dependent conductivity of a 500A YBCO/2OOA PBCO/YAIO3 film at 4.2 K.

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30 1.05 Photon Energy (meV) 10 20 30 40 50 60 70 1.00 (D o c o "o 0.95 _© M— 0) Of 0.90 0.85 H — i — I — — h -I— I — \ — — \ — I — I — h I I I I I 1.00 o c o "o 0.95 (D 0.90 0.85 5000A YBC0/SrTi03 T = 4.2 K 0 Tesia 3 TesIa 6 TesIa 12 TesIa 17 TesIa JL -1 I 1 i_ 100 200 300 400 500 Frequency (cm"^) 600 Fig. 6 The measured zero-field reflectance (upper) of a 5000A YBCO/SrTiOa film at 10, 70, and 100 K. (Lower) displays the reflectance spectra at 4.2 K as a function of magnetic field.

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31 Photon Energy (meV) 10 15 20 0 5 10 15 20 1.5 o "5^ 1.0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 r \uj 1 — 4.Z ^ 17 Tflsin 1R Tfl — 1 — 1 — 1 — 1 — 1 — \ — 1 — 1 — 1 — 1 — 1 — 1 — (c) T = 72 K 18 TesIa 77 Tfl^ln 1 ' 1 1 1 1 1 1 1 1 — 1 — 1 — 1 — 1 — 1 — 1 — 1 — 1 — 1 — . (d) T^= 95 K ' 18 TesIa 27 TesIa — 1 — 1 — 1 — 1 — I — 1 — 1 1 1 1 1 1 1 1 1 1 1 1 1 — 1 — 1 — 1 — 1 — 1 — J — 1_ ] 1 1 1 1 1 1 1 , , , , 50 100 150 0 50 100 Frequency (cm"') 150 200 Fig. 7 The magneto-transmittance at several temperatures and magnetic fields for a 400A YBCO/MgO film.

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32 Photon Energy (meV) 0 5 10 15 20 0 5 10 15 20 1.5 o .0 0.5 1.5 1 1 1 1 1 1 1 1 1 1 I 1 1 1 1 1 1 1 1 1 1 1 1 1 [a) 1 4.Z K 6 TesIa 12 TesIa 27 TesIa — 1 — 1 — 1 — 1 — |— 1 — |— T'T'I I r T I J TTT I j T TT \ ^D^ 1 — DU N 6 TesIa 27 Tesln 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 r 1 1 1 1 1 1 1 1 1 1 50 100 150 50 100 150 200 o "5^ 1.0 0.5 — 1 — 1 — 1 — 1 — J T — rT I 1 1 r 1 1 1 1 1 1 1 . (c) T = 70 K 6 TesIa 18 TesIa 1 1 1 I 1 1 I I 1 1 I 1 r TpT-i — 1 — 1 — . (d) T = 80 K 6 TesIa 1? TesIa 1 1 1 1 1 t r r 1 1 1 1 1 1 I 1 1 1 1 1 r 1 1 1 1 1 1 1 1 1 1 1 r 1 1 1 1 1 50 100 150 50 100 150 200 Frequency (cm" ) Fig. 8 The magneto-transmittance at diflFerent temperatures and magnetic fields for a 600 A YBCO/MgO film.

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33 Photon Energy (meV) 5 10 15 10000 -1 1 1 r (a) 500A YBCO/2OOX PBCO/YAIO600 I I I I J I I I I I E o I G 8000 6000 4000 2000 0 100 200 300 Temperature (K) 20 K 100 K 300 K dc Fit -I 1 I i_ -1 1 L. 50 1 00 Frequency (cm~^) 150 Fig. 9 The real part of the optical conductivity (in dots and symbols) of (a) a 500A YBCO/2OOA PBCO/YAIO3 and (b) a 400A YBCO/MgO films. The solid curves are fit to the data using a two-component model for the dielectric function. The square symbols on the vertical axes show the dc conductivity values. The inset shows the temperature dependence of Drude scattering rate, l/ro, obtained from the fit.

PAGE 42

34 Photon Energy (meV) 0 10 20 30 1 5000 I — I — I — I — 1 — I — I — I — 1 — I — I — I — I — I — I — I — I — I — I — I — I — I — ' — I — I — I — I — I — I — I — I — I — I — I — I — I — r (b) 400^ YBCO/MgO I 0 100 200 300 ^ Temperatura (K) o 7 250011Q I — I — I — I — I — I — I — I I I I I 1 I I I I I I I I I I I I I I I I I 0 50 100 150 200 250 300 Frequency (cm~^) Fig. 9-continued

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35 Photon Energy (meV) 5 10 15 5000 -1 1 1 rYBojCujOy.^ films 4000 500A YBCO (T = 20 K) 400A YBCO (T = 10 K) 3000 _i 2000 1000 -J 1 I I -1 i I I 50 1 00 Frequency (cm~^) 150 Fig. 10 The superconducting penetration depth of a 500A YBCO/200A PBCO/YAIO3 film at 20 K and a 400A YBCO/MgO film at 10 K.

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36 20 40 60 80 100 Temperature (K) Fig. 11 Magnetic phase diagram for YBCO films. The solid and dashed lines represent the H T diagram obtained from dc transport and / V measurements.^^'^" The dotted-dashed line represents the expected Meissner phase. The square and triangular symbols are the magnetooptics data for 400 and 600A YBCO fihns, respectively. The open symbols represent H and T values where the change in transmittance from the zero-field value was small or zero (less than 2 %) whereas the filled symbols represent H and T values where the change in transmittance with field was large (greater than 5 %).

PAGE 45

CHAPTER III DOPING-INDUCED CHANGE OF OPTICAL PROPERTIES IN UNDERDOPED CUPRATE SUPERCONDUCTORS Introduction The subject of normal state properties in the underdoped highTc superconductors has received a great deal of attention recently. ^'^ This interest is exemplified by the socalled "normal-state pseudogap" phenomenon observed in several different experimental techniques. The nuclear magnetic resonance (NMR)^^~^^ and neutron-scattering measurements^^'^^ first suggest the opening of a gap in the spin excitation spectrum on normal-state underdoped YBa2Cu307_i (Y123) and YBa2Cu408 (Y124). Meanwhile, for these underdoped materials, the in-plane resistivity is linear only above temperature T*, which itself is well above Tc.^^""^^ Furthermore, angle-resolved photoemission spectroscopy (ARPES) experiments'^2-74 underdoped Bi2Sr2CaCu208 (Bi2212) indicated the presence of a gap in the charge excitation spectrum at certain locations on the Fermi surface at temperatures above Tc. Indications of normal-state, gap-like anomalies in underdoped cuprates have also been observed in infrared optical measurements as well.'^^"^'' The c-axis spectra of underdoped Y123"''^^ and Y124^^ have conductivity depression below 400 cm'^ interpreted as the result of the formation of a pseudogap. This spectral structure appears at a temperature scale which matches the spin susceptibility determined from the NMR measurements and has been discussed in the context of the spin gap. In contrast, a pseudogap is not evident in the optical conductivity measured in the Cu02 planes. Instead, there is structure in the l/r(u;, T) in the a6-plane, a depressed 37

PAGE 46

38 scattering rate at low frequencies and at temperatures a little above TcJ*"*** The shape of the normal-state and the superconducting-state 1/t{lo,T) are very close. There aie several open questions about this normal-state pseudogap. First, the energy of the pseudogap-like structure does not change with doping. It is commonly observed at 400 cm~^ in the c-axis conductivity and around 700 cm~^ in the a6-pl«ine scattering rate. Also, it is imclear why there is apparent factor of 2 between these two energy scales. Second, the doping independence of the energy is in strong contreist to the behavior of spin gap temperature, which decreeises with doping. Third, in the normal state cri{uj) exhibits a much larger spectral weight at high frequencies than would be present from the generalized Drude form with a frequency-dependent lifetime. In order to address the issues mentioned we have measured the a&-plane reflectance of single crystals of Y-doped Bi2212 and Pr-doped Y123 with changes in carrier densities at doping level ramging from heavily underdoped to necirly optimally doped. Optical investigations, extending over a broad frequency range and at various temperatures, offer an effective way to study the energy and temperature dependence of intrinsic parameters characterizing these materijJs. We first describe a number of properties: the reflectcince spectrum, the optical conductivity, and the effective ccirrier density. We then discuss how they might accovmt for the evolution of the a6-plane spectrum with doping. Next, we focus on the low-frequency conductivity and spectral weight of a strongly underdoped Bi2212 sample {Tc = 35 K) in the whole temperature range. We investigate whether the normal-state pseudogap leads to a change of the charge excitation spectnun that can account for the observed dc resistivity. Of particular relevance in this connection, is the identification of the energy and temperature dependence of the quasiparticle damping. We derive the scattering rate from both the one-component and the two-component pictures. In

PAGE 47

39 one-component analysis, our results have been treated within the framework of the generalized Drude model and the marginal Fermi liquid theory.^^'*^ Depending on the model, we compare the different features in the scattering rate deduced &om the spectra. To the end, considering the superconducting response for all doping level studied, observation of a superconducting gap has been a hotly disputed issue. Even though we cannot say anything definite about the superconducting gap in all our spectra, the amount of conductivity that condenses into the S function at or = 0 is given less ambiguously from infrared measurements. Our discussion concentrates on the relation between the transition temperature and the number of carriers in the superfluid or the total number of carriers. Experiment Sample characteristics The experiments described here have been done on Bi2212 and Y123 single crystals. In these systems, there are two ways to reduce the carrier concentration on the Cu02 planes, and, thus prepare imderdoped samples. One is to substitute an element in the crystal structure by another one with higher valence state. In this case the substitution of for Ca^+ has been found to be most efficient in Bi2212.*' Heavily underdoped Bi2212 samples with = 35 K (Pb 50%, Y 20%), 40 K (Y 35%) were measured. Another way is to remove oxygen from the pure seimples. By annealing the crystals in argon, one slightly underdoped Bi2212 with Tc = 85 K was obtained. Details of sample preparation are reported elsewhere.** In the Y123 system, we studied three fully oxygenated Yi_iPriBa2Cu307-6 single crystals. Substitution of Pr for the Y atom in Y123 changes only the hole content in the Cu02 planes, while the structure of the CuO chains remains unaffected.*^ The Pr-doped samples have a Te

PAGE 48

40 of 92, 75, and 40 K, respectively, for x = 0, 0.15, and 0.35. The crystals were grown by a method described elsewhere.^^ The dc-resistivity measurements as a function of temperature on five samples are depicted in Fig. 12. The resistivities of Bi2212 and Y123, with a Tc = 85, 92 K respectively, follow a linear ciirve over a wide temperature range. At 300 K, the increase of the resistivity with Y or Pr doping is apparently due to the reduction of the carrier concentration, although disorder introduced by the doping may also contribute to this increase. Interestingly, as in all doped samples, the overall resistivity still shows metallic-like behavior down to the transition temperature. However, there is a characteristic change of slope dp/dT at temperature T* marked by arrows. The values of T* increase with increasing Y and Pr doping. This feature is similar to the one observed in imderdoped Y123 by oxygen removal^^ and Sr-doped La2_j;SriCu04 (La214).*^'*^ Since it is unlikely that the nimaber of Ccirriers increase below T*, it appears that the temperature dependence of the normal-state resistivity p = (m/ne'^)(l/r) must be attributed entirely to the scattering rate. Thus, a slop change in the resistivity blow T* indicates a change of carrier scattering at low temperatures. Optical measurements The optical reflectance of all crystals has been meeisured for the radiation polarized parallel to the a6-plane over 80-40000 cm~^ (10 meV-5 eV). In the high frequency range (100040000 cm~^) range we use a Perkin-Elmer 16U grating spectrometer while the farand mid-infrared (80-4000 cm~^) regions were measured with a Bruker IFS 113v Fourier transform spectrometer. For the later frequencies, the temperature of the sample was varied between 300 and 20 K by using a continuous-flow cryostat with a calibrated Si-diode thermometer mounted nearby. Determination of the absolute value of the reflectance was done by coating the sample with a 200GA film of Al after measuring the uncoated sample. The spectra of the uncoated sample were then

PAGE 49

41 divided by the obtained spectrum of the coated sample and corrected for the know reflectance of Al. The accuracy in the absolute reflectance is estimated to be ±1%. The optical properties {i.e., the complex conductivity ) + tf2('*^)) have been calculated from KramersKronig analysis of the reflectance data. The usual requirement of the KramersKronig integrals to extend the reflectance at the lowand high-frequency ends was done in the following way. At low frequencies, the extension was done by modeling the reflectance using a Drude-Lorentz model and using the fitted results to extend the reflectance below the lowest frequency measured in the experiment. The high-frequency extrapolation were done by merging the data with results from the literature®^ or by using a weak power law dependence, ^ ~ a;~* with s ~ 1-2. The highest frequency range was extended with a power law ^ ~ a;"*, which is the free-electron behavior limit. Results Roomtemperature spectra Figure 13 shows the room-temperature afr-plcine reflectance of the six crystals over the entire spectral rcinge. Note the logarithmic scale. The reflectance of each Scimples drops steadily (but not quite linearly) throughout the infrared, with a sort of plasmon minimum around 8000-15000 cm~^ in all cases. What is notable about the two highest Tc crystals of Bi2212 and Y123 is that they show high values of reflectance over 90% for uj < 1000 cm~^. For the doped samples, with reduced the carrier concentration on the CuOj planes, the reflectance in the whole infrared region is substantially decreased. As a consequence, a few infrared-active phonons in the a6-plane are visible. However, this reduction of the Ccirrier density hcis little effect on the frequency location of the plasmon minimum. It is interesting to note that there is a shoulder at aroimd 4000 cm~^ in Y123 systems, which is probably Jissociated with

PAGE 50

42 excitations on the 6axis-oriented chains. This is in accord with the measurements on single-domain Y123 crystals. The real part of the conductivity cri{uj), obtained from KramersKronig analysis of the reflectance, is shown in Fig. 14. The a6-plcine optical conductivity spectra of the Bi2212 and Y123 near optimal doping have several common features. There is a peak at a; = 0 and a long tail extending to higher frequencies in the infrared region where (T\(u}) falls as a;~\ slower than a;"'^ decay of a Drude spectrum. At higher frequencies, we observe the onset of the charge-transfer absorption at about 14000 cm~\ which corresponds to the optical transition between the occupied 0 2p bcind and the empty Cu 3d upper Hubbard band. Other interband transitions also appear above 20000 cm~^. In the reducedTc samples, as suggested by the reflectance data in Fig. 13, there is a lot of spectral weight lost in the infrared region. Significantly, the weight lost below the charge-transfer absorption band is transferred to the higher frequencies. Note that the Y123 crystals show a bump-like structure around 4000 cm~^ on account of the excitations in the chciius mentioned above. Finally, weak phonon modes, which are not completely screened by the free carriers, are seen in the far-infrared. Additional information about the electronic structure ccin be extracted from the oscillator strength sum rule.^*' The effective nimaber of carriers participating in optical transitions for energies less than ku is given by 0 where m* is the effective mass of the carriers, m is the free-electron mass, Vc^a is the imit cell volume, and iVcu is the the nimiber of CuO layers per unit cell. Here, we use Ncn = 2 for all measured twinned single crystals. The effective mass is taken as the free-electron value. A plot of iVeff (u;) per planar Cu atom is shown in Fig. 15 on a linear

PAGE 51

43 scale. For the crysttils with high dc conductivity, Nen{^) at first increases steeply at low frequencies, on account of the appearance of a Drude-like band centered at w = 0, and continues to increase in the mid-infrajed region. iVeff(a;) exhibits a plateau in the interval between 6000 and 12000 cm~^ Above 12000 cm~^, the remaining charge-trcinsfer excitation and higher frequency transitions contribute iVeff(a;). As expected, the decreasing A^effC'^) over a wide frequency range was observed in the low Tc samples. However, all iVef (w) curves come together above 30000 cm~^ This shows that, as reducing carrier numbers, the low-frequency spectral weight shifts to high frequency but the total weight does not change below 30000 cm~^. Indeed, the redistribution of the spectral weight in the Cu02 planes with doping have been observed for Sr-doped La214^^ and oxygendeficient Y123^^'^^ as well. Temperature dependence in the infrared The temperature dependence of the a6-plane infrared conductivity is shown in Fig. 16. The optical response of all samples is metallic, i.e., when the temperature is lowered from 300 K, there is an increase in (Ti{uj) at the lowest frequencies, in accord with the dc resistivity. As mentioned above, for T > Tc(T\ {u) is strongly suppressed in underdoped samples over the entire infrared frequency range. Nevertheless, the conductivity below 300-400 cm~^ remains approximately Drude-like: a zero-frequency peak which grows and sharpens as temperature is reduced. The temperature dependence at frequencies above 1000 cm~^ is relatively modest; it is in fact mostly due to a narrowing of the Drude-like peak at zero frequency. Below Tc, we observe that there is a transfer of oscillator strength from the far-infrared region to the zero frequency ^-fxmction response of the superconducting condensate.^* The spectral weight lost at low frequencies in the superconducting state is large in the nearly optimally doped samples while in the most imderdoped samples it is very small. It shoidd be noted

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44 that for all doping level studied, at 20 K, there remains a pronounced conductivity at low frequencies, suggesting no sign of a superconducting gap. Figure 17 shows the reed part of the dielectric function at three temperatures below 2000 cm~^ The rapid decrease in ei(a;) of ah the samples at low frequency with decreasing temperature is an indication of the metallic behavior (characteristic of free Ccirriers). In a purely Drude system, the zero crossing corresponds to the location of the screened plasma frequency, Up = (j^p/y/^^o where Cqo is background dielectric associated with the high frequency interband transitions, and the plasma frequency u}p is related to the carrier density n through Up = y47rne^/m*. However, the cuprates are not simple metcils, juid the presence of a number of excitations in the mid-infrared will tend to shift the zero crossing to a lower frequency. Thus, estimate of carrier density should be made from iVeff(a;) instead of Up. As the temperature is lowered below Tc, shows a Icirge negative value, implying that the inductive current dominates over the conduction ciirrent in the superconducting state. Here, the dielectric function looks like that of perfect free Ccirriers; ei{w) = Coo — ^ps/^'^ where u)ps = ^J^irnse^ fm* is the superfluid plasma frequency and n, is the superfluid density. The reduced is quite evident in the doped samples in the Fig. 17. Discussion Low-frequency spectral functions As noted previously, ARPES experiments^^"^* on imderdoped Bi2212 crystals in the normal state revealed the existence of a pseudogap in the charge excitation spectrtun-a suppression of spectral weight with a residual intensity on the Fermi level. For a next step, in order to investigate the influence that the pseudogap has on the peculiar charge dynamics of the Cu02 planes, we present a complete set of temperature-dependent data in the most underdoped Bi2212 with Tc = 35 K.

PAGE 53

45 Our other undedoped Bi2212 and Y123 samples gave similar results. We emphasize two important spectral fimctions, the real part of the conductivity (Ti{u},T) and a dimensionless measure of spectral weight iVefF(u;,T). Optical conductivity . The temperature evolution in (T\{u), T) is shown in Fig. 18. In the normal state, cri{u},T) approaches the ordinary dc conductivity at low frequencies (The dc conductivity is shown on the vertical axis as filled squares). At the same time, we observe a narrowing in the far-infrared conductivity at low temperatures, whereas at higher frequency, cri(w) does not show much temperature vaxiation. If there is indeed the formation of an energy gap at the Fermi surface in normal-state superconducting cuprates at low hole densities, from ARPES, at least in underdoped Bi2212, the corresponding optical conductivity spectrum should exhibit a bump-like structure. The situation must be similar to aji interband trzinsition like the chargetransfer band in the cuprates. Note also that the opening of a pseudogap in the electronic spectrum is clearly seen in the c-axis conductivity of Y123 and Y124.'^^" In contrast to this, no distinct features have been observed in infrared a6-plane , T) in Fig. 18. In the normal state, the spectreil weight associated with the free Ceirriers shifts to lower frequency with decreasing temperature, on accoimt of the sharpening of the Dnide-like peak in «Ti(t«;). This is reflected in the rapid increase in the value of iVejf (w, T) at low

PAGE 54

46 frequency. A more detailed look of the temperature dependence of the low-frequency spectral weight is given in the inset of Fig. 19. We plot the difference in iVgff (w, T) computed in the 300 K and other lower temperatures for uj = 250, 500, 1000, and 2000 cm~^. Again, the gradual increase of the spectral weight is observed at each frequency from 200 to 75 K. If there were pseudogap to develop in the charge carrier excitation spectrum of underdoped Bi2212, as suggested by ARPES measurements,^^"^* one would expect an influence on the low-frequency spectral weight from the gapping some of the carriers at particular parts of the Fermi surface. This modification of the Fermi surface should give rise to the redistribution of low frequency spectral weight. In contradiction to this expectation, we do not find any significant change in the normal-state curve as temperature is reduced, other than the cdready mentioned shift to lower energies. In contrast, the iVeff(u;, T) curve for the superconducting state does indeed show a reduction of spectral weight compared to the normal state. The missing area in the (Ti{u,T) in the superconducting state appears in a ^-function at a; = 0, and this contribution is not included in the numerical integration which yields Ne«{uJ,T). Therefore, the difference between Ncf[{uj, T) above and below Tc is a measure of the strength of the S function, cind is proportional to the spectral weight in the superfluid condensate. Dielectric function models In analyzing the a6-plane optical spectra of highTc materials, there has been much discussion over the one-component and the two-component pictures used to describe the optical conductivity.* In the two-component analysis, there are assimaed to be two carrier types: free carriers which are responsible for the dc conductivity and which condense to form the superfluid below Tc, and bound carriers which dominate the midinfrared region. Thus, the cri(a>) spectrum is decomposed into a Drude peak at a; = 0 with a temperature dependent scattering rate and a broad mid-infrared absorption

PAGE 55

47 band centered at finite frequencies, which is essentially temperature independent. An example of this approach is to fit the data to a Drude-Lorentz model dielectric function Jl N 2 e(a;) = + V f-. + eoo, (6) where ujpj) and l/r/j axe the plasma frequency and the scattering rate of the Drude component; uj, "yj, and Upj axe the frequency, damping, and oscillator strength of the jth Lorentzian contribution; and Cqo is the high frequency limit of c(a;) which includes interband transitions at frequencies above the measured range. The alternative, a one-component picture, has only a single type of carrier; the difference between midand fai-infrared response is attributed to a frequency dependence of the scattering rate and effective mass. As an empirical approach one can use the generalized Drude formalism C(U') = Coo . , (7) a;(w -I17(0;)) where is the bare plasma frequency of the charge Ceirriers, and 7(0;) = 1/t{u>) — iu}X{uj) is the complex memory function. The quantities 1/t{uj) and A(w) describe the frequency-dependent (umrenormalized) carrier scattering rate and mass enhancement so that the effective mass is given by m*{uj) = m(l -|A(a;)). A one-component model also comes from the ideas of non-Fermi-liquid behavior of the high-Tc superconductors, as introduced by Varma et a/.*^'^^ in the "marginal Fermi liquid (MFL)" theory and Virosztek and Ruvalds^^'^* in the " nested Fermi liquid (NFL)" theory. In the MFL, the dielectric fimction is = u,[u,-22(c./2)) ' where S(a;) represents the complex self-energy of the quasiparticles, and the factors of 2 arise because quasipeirticle excitations come in pairs. The real part of S is related to

PAGE 56

48 the effective mass m* by m*{uj)/'m = 1 —2 Re T,(u)/2)/uj whereas the imaginary part of S is related to the quasiparticle lifetime through l/r*(a;) = — 2m ImE(a;/2)/m*(u;). The basic assimiption of these theories is that there exists an anomalous charge or spin response (or both) for the cuprates. It is worth mentioning that other microscopic theories, such as the "nearly antiferromagnetic Fermi liquid (NAFL)" theory proposed by Monthoux and Pines^^ and the "phase-separation model" advocated by Emery and Kivelson,^"" all lead to a similar picture. The self-energy, S, of the charge carriers (essentially the scattering rate) should taJse the form, -ImS(a;)~-j (9) where Xt or X^^ is a dimensionless coupling constant. Hence, for a; < T the model predicts a renormalized scattering rate that is linear in temperature, which agrees with the linear temperature dependence in the resistivity that is observed in nearly all copper-oxide superconductors. As u) increases, reaching a magnitude of order of r, interaction of the charge carriers with a broad spectrum of excitations comes to dominate the response. This causes Im S(u;) to grow linearly with frequency, up to a cutoff frequency Uc that is introduced in the model. The functions 1/t{u), m*{u)/m, and -ImS(a;) etc. can all be calculated from the Kramers-Kronig derived dielectric fimction. In doing these calculations, we have used the bare plasma frequency values of Up, calculated from the conductivity sumrule analysis in Eq. 5 with integration of cri(a>) up to the charge-transfer band. The values of e^o axe obtained from fitting the low-frequency reflectance data below the charge transfer gap by using a Drude-Lorentz model. In the following section, we will discuss the behavior of the quasiparticle scattering rate from these different points of view.

PAGE 57

49 Qucisiparticle scattering rate Generalized Prude model . First, let us focus on the frequency-dependent scattering rate, shown in Fig. 20, extracted from the generalized Drude formcJism using Eq. 7. Starting with the Bi2212 crystal with Tc = 85 K, we find that the room temperature 1/t{uj,T) is linear up to 2000 cm~^. When the temperature is reduced from 300 K to 200 K, the high frequency part of 1/t(u;, T) gently decreases and still exhibit nearly linear frequency dependence while below 800 cm~^ the scattering rate 1/t{u},T) fcJls faster than lineaxly. The suppression in 1/t{u},T) at low frequencies is cleaily resolved at lower temperatures. Similar feature has been previously observed optically and even discussed in relation to a pseudogap state. At 20 K, the low-frequency 1/T(a;, T) drops more sharply, although to use a Drude formula in the superconducting state does not seem correct. Upon decreasing the carrier density in Bi2212, Tc = 40, 35 K, the frequencyand temperature-dependent behavior in 1/t{u,T) is more astonishing. The absolute A^ue of the 300-K 1/7(0;, T) increases at high frequencies. Unlike the case of the nearly optimally doped Bi2212, a distinct suppression of 1/7(0;, T) is observed over the whole temperature range. The position where l/r(o;, T) deviates from being the linear in o; seems to move towards higher frequencies, and the depth of the normalstate threshold structure also increases as well. It is worthwhile to mention that above 1000 cm~^ the absolute value of the scattering rate in the Y 35%-doped Bi2212 is somewhat higher than that in the Pb 50%, Y 20%-doped sample. One possible explcination is that additional scattering mechcinism, which originates from the baxis superlattice structure of Bi2212, is removed by the Pb doping. Nevertheless, we would like to point out that the shape of the normal-state and superconducting-state 1/t{u},T) looks very similar in these heavily underdoped Bi2212.

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50 The 1/t{u,T) spectra for Y123 are shown in the lower panels of Fig. 20. We begin with the Y123 crystal with Tc = 92 K. At 300 K, the high-frequency 1/t{u},T) is approximately lineax, with a deviation from linearity below 800 cm~^. At lower frequencies we also observe a small upturn in the 1/t{u),T) spectra. As similar to the case of Bi2212, the scattering rate is suppressed more rapidly at low frequencies (a; < 800 cm~^) when temperature is reduced. Upon entering into the superconducting state, the low-frequencies 1/t{u},T) is depressed significantly. With 15% Pr substitution (Tc = 75 K), the overall magnitude in 1/t{u!,T) is increased somewhat and the amount of change with temperature is diminished. In general, the l/r(w,T) shows similar behavior to the nearly optimal doped Y123. When the Pr content is increased to 35 % {Tc = 40 K), the scattering rate is strongly enhanced at all frequencies. The frequency dependence of l/r(w,r) is also modified as well. In particular, the slope of 1/7(0;, T) becomes negative at higher frequencies, with a maximiun neax around 1200 cm~^ It is, moreover, remarkable that there is a resemblance in 1/t{u},T) between the spectra obtained at 20 K and at T > Tc. Marginal Fermi liquid ancilysis . Figure 21 shows the imaginary part of the selfenergy for Vcirious doping and temperatures, calculated using the MFL formula in Eq. 8. For the nearly optimally doped Bi2212 and Y123, the 300-K -ImS(a;,r) spectra increase with frequency in a quasilinear fashion though a small deviation from linearity below 400 cm~^ is observed in Y123. As the temperature is lowered, a threshold structure develops at low frequencies and becomes progressively steeper with the decrease of temperature while the temperature dependence is rather small in the high frequency part of — ImS(a;,r). The difference between the room-temperature and the superconducting-state ImS(u>, T) is prominent at low frequencies. When carrier density is decreased, deviations from linear behavior appear, even at room temperature; moreover, the shape of the normal-state Im S(a;, T) becomes similar to that

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51 in the superconducting state. It is important to note that the frequency scale associated with the suppression of — ImS(a;,r) does change with doping. For the most underdoped scimples with Tc = 35, 40 K, the normal-state depression of — ImS(u;, T) occurs at u; < 800 cm~^ As the doping level is increased towards the optimal, the onset frequency related to the changes of — ImS(u;,r) is about 400 cm~^. Qualitatively, as shown in Eq. 9, there are two regimes to consider for the — ImS(u;, r) function, i.e., ui < T and u > T. We obtained the coupling constants \t = 0.4 ± 0.02 and 0.5 ± 0.1 in the regime a; < T for the nearly optimally doped Bi2212 and Y123. Furthermore, from evaluation of the slopes in the region where -ImS(a;,r) is linear in u, it is found that at 300 K A^, = 0.20 ± 0.01 in Bi2212 and A^, = 0.26 ± 0.05 in Y123. At 100 K these numbers are a factor of 2 larger. Note that our data is linear only below the cutolF frequency Uc = 1200 cm~^ Much more interesting are the data for the underdoped crystals. The experimented — ImE(a;, T) curves level oflF above Wc, but below ujc the slope is still larger than for the optimally doped specimens. In this respect, it appears that lowering the temperature of the sample would be eqmvalent to reducing the carrier density and, hence, to increase the coupling constant. Nevertheless, in accord with previous measurements on oxygen deficient Y123 single crystals,^^ there is an increase in the qucisiparticle interaction strength A^, with decreasing carrier concentration. These results are diflfictdt to understand within a MFL perspective, because they imply that the lower Tc materials have a larger A^. The difficulty comes because the Tc is also supposed to be determined by A^,. Thus, strong coupling means larger A^, and it should give rise to higher Tc. Finally, it is important to recall that the energy scale associated with the principal features in the Im S(u;, T) spectra obtained from the MFL analysis are all about two times smaller than the value in the l/r(a;,r) spectra by using the generalized Drude approach. This factor occurs because the MFL theory assumes

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52 the quasiparticle excitation occurring in pairs, whereas a single excitation, such as a phonon or magnon, is assumed in the generalized Drude model. Two — component picture . A completely dilferent point of view is taken by the two-component picture. In this analysis, we have to subtract the mid-infrared absorption to obtain the Drude term or to fit to a combination of Drude and Lorentzian oscillators; given in Eq. 6. Figure 22 shows the zero-frequency scattering rate of the free-ccirrier or Drude contributions as a function of temperature from such an analysis, when T > Tc, I/tj) veiries linearly with temperature (together with em essentially temperature-independent Drude oscillator strength) for all the doping level studied. Such a temperature linear behavior in I/tj) above Tc has been observed earlierly in the optimally doped cuprates.^^'^'^'^''^ We write h/ro = lirXoksT + ft/ro,^°^ where Ax) is the dimensionless coupling constant that couples the chaxge carriers to the temperature-dependent excitations responsible for the scattering, and shows in Table 2, the values of Upo, Xj), and I/tq. All the samples show a normal-state I/tj) linear in T, with all about the same slope, giving A/j ~ 0.2-0.3. The fit is shown as the soUd line. This is remarkable: despite the huge difference in Tc, the coupling constcint Ap is the same in these materials. They differ only in their intercept, which is a measure of the residual resistivity of each sample. The residual resistivity can cdso be seen in the data in Fig. 12. Below Tc, l/r^j in all studied samples shows a quick drop from T-linear behavior, which has been pointed out previously in the optim
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53 linear regime above Tc. Tliis behavior could imply that the superconducting-state quasiparticle scattering rate is governed by the impurity effects. Another viewpoint is based on the node (zeros) of the gap fimction, and then the scattering rate reflects the response of the quasiparticle states with small excitation energies. Table 2. Drude plasma frequency, ujpD, coupling constant, A/j, and the zerotemperature intercept, I/tq, for six materials. Materials Tc{K) ujjiD ( cm~^) A/? 1/ro (cm-i) Bi2Sr2CaCu208 85 9000 ± 200 0.28 9 Y35% 40 5600 ± 200 0.20 85 Pb 50%, Y 20% 35 6100 ± 200 0.20 185 YBa2Cu307-« 92 9800 ± 200 0.26 2 Pr 15% 75 8700 ± 200 0.25 135 Pr 35% 40 6800 ± 200 0.26 252 Compare with dc transport. It is interesting to compare the scattering rate with the dc resistivity data. The most striking feature in Figs. 20 and 21 is that both the normal-state l/r(w, T) and — ImE(a;,T') spectra show a threshold structure at low frequencies in the underdoped materials. When the doping reaches the optimal level the threshold structure is weakened. The dc resistivity in Fig. 12 of underdoped crystals is linear function in T for T > T*, but shows a crossover to a steeper slope at r < T*. If the temperature dependence of the normal-state resistivity p = (m/ne^)(l/r) is attributed entirely to the scattering rate, then the crossover behavior could be attributed to the low-frequency suppression of the scattering rate. As discussed already, this view is further supported by many experimental observations showing that the pseudogap state develops at T < T* in the underdoped compounds. However, in this connection we should remark on a discrepancy between the scatter-

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54 ing rate and the pseudogap state. As shown in Figs. 20 and 21, it must be recognized that a threshold structure exists already at room temperature in the imderdoped samples even though all dc resistivity curves exhibit a linear T dependence from 300 K to r*. Moreover, when a pseudogap opens, the amount of low-energy scattering decreases, implying that the absolute value of the scattering rate in the sample should be lower than that without a pseudogap state. Our experimental observations «ire not in accord with this expectation. First, cis shown in Fig. 22, the two-component analysis shows that the linear-T behavior in I/tq was foimd in all samples. Second, the decreased scattering rate is nearly the same independent of whether the pseudogap is expected or not. Third, the limited number of points and possible uncertainties specially below 100 cm~^ prevent us to determine whether the observed deviation from linearity below T* in dc resistivity data is consistent with our present results in 1/t£). However, a strong suppression in scattering, as suggested by the 1/t{(jj,T) and — ImS(a;, T) results, is ruled out. Superconducting response Superconducting gap . The superconducting gap and the nature of the superconducting condensate are two fundamental quantities which characterize the superconducting state. An ordinary 5-wave superconductor has a gap A in its excitation spectrum, which causes cri{u)) to be zero up to a; = 2 A; above this frequency (Ti{u>) rises to join the norm^J-state conductivity.^"^ Furthermore, structure in <7i(a>) at 2A -Iflo reflects peaks at fio in the effective phonon-mediated interaction a^F(n), and a detailed measTirement of
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55 reasons, the seeirch for evidence of a superconducting gap in highTc materials has proven difficult. First, gap anisotropy can lead to broadening of the absorption edge
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56 not produce dirty-limit behavior as seen in conventional superconductors — an onset of absorption at 2 A. Instead, a new lowfrequency, Dnide-like, absorption appears in the superconducting state, taJdng spectral weight away from the superconducting condensate. This observation could be also due to the unconventional nature of the response of the highTc superconductors. If a d-wave gap is a possible scenario, the low-frequency absorption will be enhanced in a dirty sample. Superfluid density. Although there is still a lot of controversy about the experimental data and their interpretations regarding optical studies the superconducting gap in the cuprates, the spectral weight or oscillator strength of the superconducting condensate is given less ambiguously from infrared measurements. A superconductor has a low frequency ai{uj) that is a
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57 The superconducting penetration depth is a related parameter, which we axe naturally led to associate with the superfluid density. It is a direct measure of the density of carriers n, condensed in the superconducting state «ind through its temperature dependence, the symmetry of the superconducting order parameter can be discriminated. The penetration depth is usually determined by the experiments of muonspin-rotation (^SR), DC magnetization, and surface impedance in the microwave and millimeter wavelength region. The later two methods, while yields the temperature dependence of the penetration depth with great accuracy, generally can not be used to obtain its absolute value. In the case of infrared measurements, the penetration depth can be found from KramersKronig analysis of the reflectance data, which gives the imaginary part (T2{u)) of the complex conductivity as well cis the leal part
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58 where o-i„(u;) and (tis{uj) are the real parts of the complex conductivity at T w Tc and T «C Tc, respectively. Equation 11 states the spectral weight lost at low frequencies in the superconducting state has been transferred to the zero-frequency ^-function response of the superconducting condensate. This missing spectral weight from the sum rule is indicated by solid squares in Fig. 24. The values of penetration depth of all samples obtained by Eq. 11 are displayed in Table 3. Generally speaking two estimates for Xi in Eqs. 10 and 11 agree within about 10%. The penetration depth is related to the plasma frequency of the condensate by, A/, = c/(jps. The values of u)pS obtained directly from the dielectric function ei(u;) or through the simi rule agree well. Spectral weight above and below Tc. We now turn to a comparison among the various contributions to (T\{u}), above and below Tc. We have used finite-frequency siun-rule analysis in Eq. 5 and then calculated the eflFective number of Ccirriers per pleinar Cu atom in the low frequency region below the charge-transfer gap as ^tot> the Drude or free carrier part (from two-component analysis) as iVorude? the superconducting condensate weight as Ng. Results for our Bi2212 and Y123 systems together with oxygen doped La2Cu04.i2^" (La214(0))and fully optimal Tl2Ba2CaCu208"^ (T12212) are summarized in Table 4. A^s is also shown as a fraction of iVtot and iVorudeNotably, there is an "universal correlation" between the numbers of carriers and the transition temperature. This link holds whether one considers the niunber of Ceirriers in the superfluid or the total number of carriers. In Fig. 25 we plot Tc versus ntot for high-Tc superconductors, where ntot = Nxot • i^Cu/KeU-^^^ One Bi2212 sample has Tg = 68 K by Ni 4.3% substitution. In addition, one point hcis cdso been included for the a superconductor oxide that is not based on Cu02 planes, Bai-iKxBiOs (BKBO) with Tc = 28 K.^^* All of the data points follow an approximately common line. In the conventional superconductors an increased carrier density norm
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59 increased TcA similar trend has been observed for the cuprates at the doping level in the underdoped and optimal doped regime. Interestingly, a recent study^^^ on the optical conductivity of highTc superconductors from underdoped to overdoped range points out that in the underdoped regime progressive doping indeed increases the low-frequency conductivity spectral weight while this trend does not continue to the overdoped part of the phaise diagrcim. It is argued that there is an increase in the carrier density as Tc is increasing, and overdoping decreases Tc but does not lead to an increase in the toted number of carriers. Another important point from the vtilues of iVtot is that in a simple rigid-band picture, the total nimaber of doping carriers corresponds to the volume enclosed by the Fermi surface. This interpretation, however, runs into a discrepancy between optical and photoemission determinations of caxrier number. Recent ARPES measurements of Bi2212^^^ ranging from imderdoped to overdoped infer large Luttinger Fermi surface, consistent with iVtot = 1 -f a; where x is the dopant concentration. In contrast, optical measurements imply that iVtot = x cind we always see small Fermi surface for all doping levels studied. Figure 26 shows the relation between Tc and n,, where n, = iY, • Ncn/VceH^^^ The most striking finding in the plot is that for the underdoped and optimally doped cuprates (filled symbols) the superfluid density increeises roughly proportionally to the transition temperature. Our opticid data points follow what is generally referred to as the Uemura line. These results suggest that, regardless of charge or impurity doping, it is the parameter n, that determines Tc of the cuprate superconductors. As is well known from the /iSR measurements (open symbols), there is a "universal correlation" between Tc and n, in many cuprate superconductors: Tc increases linearly with n, (solid line) with increasing ctirrier doping in the underdoped region, then shows saturation in the optimumTc region.^^^'"® In the overdoped Tl2Ba2Cu06 (T12201) systems, both Tc and n, decrease (dashed line) with increasing hole dop-

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60 Table 4. Effective number of carriers per planar Cu atom. Materials Tc{K) iVtot ^Drude Ns La2Cu04.i2 40 0.14 0.035 0.028 20 80 Bi2Sr2CaCu208 85 0.38 0.105 0.092 24 88 Y35% 40 0.21 0.040 0.020 8 50 Pb 50%, Y 20% 35 0.23 0.050 0.017 7 34 YBa2Cu307-« 92 0.44 0.093 0.082 19 89 Pr 15% 75 0.38 0.073 0.054 14 74 Pr 35% 40 0.25 0.045 0.020 8 44 Tl2Ba2CaCu208 110 0.54 0.13 0.115 21 88 Typical uncertainties 2 ±.03 ±.01 ±.01 ±1% ±4% ing,^^^'^2° bringing the trajectory in the Tc versus n, back to the origin. We are presently unaware of any optical analysis on the evolution of superfluid density in the overdoped cuprates, so this subject will be addressed in future work. Finally, considering the superconducting condensate fraction in Table 4, we found that in all optimally doped materials, about 20-25% of the total doping carriers joins the superfluid; about 75-80% remains ar finite frequencies. Furthermore, if a two-component picture is adopted, then nearly 90% of the free-carrier spectral weight condenses. In other words, the oscillator strength of the ^-function is essentially the same as the Drude-like peak of the normal state, which is a clean-limit point of view. These results also indicate that the large portion of spectral weight in the normal state condenses below Tc in the optimally doped samples, while the superconducting condensate in the underdoped materials is rather small.

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61 Summaxv In summary, the a6-plane optical reflectance of single crystals of Bi2212 and Y123 has been measured over a wide frequency and temperature range. Substitution of Y for Ca atom in Bi2212 and Pr for Y atom in Y123 allowed us to study the doping range from heavily underdoped to nearly optimally doped. We have examined a variety of spectral functions from KramersKronig einalysis of the reflectance data. With the reduction of carrier concentration on the Cu02 planes, we observe there is a lot of spectral weight lost in the infrared conductivity. The weight lost below the charge-transfer absorption band is transferred to higher frequencies. We have also presented a complete spectral investigation of the most underdoped Bi2212 with Tc = 35 K. Emphasis has been placed on the features in the real part of conductivity , T) and the development of the spectral weight Neff('*') T), as the temperature of sample changes from above T* to below the critical temperature Tc. We find that the conductivity below 300-400 cm~^ is approximately Drude-like, a zero-frequency peak which grows and sharpens as temperature is reduced. At the same time, the spectral weight associated with the free carriers shifts to lower frequencies. It is difficult to relate our experimental observations to the normal-state pseudogap phenomenon. Considering the important role that quasiparticle damping has played in discerning the normal-state psedudogap features, we derive the scattering rate from both the one-component and the two-component pictures. In one-component analysis, our results have been treated within the framework of the generalized Drude model eind the marginal Fermi liquid theory.^^'*^ The appearance of low-frequency depression in the scattering rate spectrum (from previous measurements^*"*" as well as those reported here) signals entry into the pseudogap state. The energy scale associated with the principal featxires in 1/t{u,T) and — ImE(a;, T) shows a factor of 2 different. The frequency scale associated with the suppression of — ImE(u>, T) does change

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62 with doping. For the most underdoped samples with Tc = 35, 40 K, the nonnal-state depression of IinS(w,T) occurs at w < 800 cm~^ As the doping level is increased towards the optimal, the onset frequency related to the changes of — ImS(a;, T) was found to be 400 cm~^. An cilternative approach is to consider the zero-frequency 1/t£) from free-carrier contributions. We find that for all the samples studied, when T > Tc, 1/td varies linear with temperature and decreases qmckly below Tc. 1/td from inelastic scattering process puts all the samples in the weakcoupling limit (A/> ~ 0.2-0.3). We suggest that the pronounced features in the scattering rate spectrum are related to the majmer in which the data cire analyzed (onevs. two-component). It is a delicate question to ask which analysis, one-component or two-component, is more appropriated in our present study. In the superconducting state, some of the finite frequency oscillator strength in (71 (w) is removed by the superconducting transition. A finite low-lying conductivity remains below Tc. There is no convincing evidence of superconducting gap absorption in our spectra. In the case of the matericds with near optimal doping, the absence of a superconducting gap can be explcdned in one of two ways: a clean-limit picture in the two-component model or the presence of an unconventional gap with nodes somewhere on the Fermi surface. However, our underdoped (dirtier) samples again show no sign of a gap, which favor the latter argument. In determining the cimount of oscillator strength that condenses into the ^-function at cj = 0, we obtain a good agreement of the values of superfluid density from the missing area by sum-rule argument with ujps, or through the superconducting penetration depth A^. The spectral weight lost at low frequencies in the superconducting state is large in the nearly optimally doped samples; a sum-rule evaluation finds that about 20-25% of the total dopinginduced Ccirriers in is the S function. In contrast, in the most imderdoped Scimples the superfluid density is very small. We have also foimd that there is an "imiversal

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63 correlation" between the numbers of ceirriers and the transition temperature. This link holds whether one considers the nimiber of caxriers in the superfluid or the total number of caxriers. Our optical results axe significant and consistent with the evidence from ^SR measurements: Tc scales linearly with rij in many underdoped cind optimally doped cuprates.

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64 Fig. 12 Temperature dependence of the afr-plane resistivity for Y-doped Bi2Sr2CaCu208 and Pr-doped YBa2Cu307_i single crystals, measured by a four-probe method. A characteristic change of slope dp/dT at temperature r* is marked by arrows.

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65 Photon Energy (eV) 0.1 1 0.1 1 T 1 — I I I I 1 1 1 1 1 — r I I I 1 1 1 1 1 — r— I 1 — I I I I 1 1 1 I I I I I M 1 1 100 1000 10000 100 1000 10000 Frequency (cm~^) Fig. 13 The roomtemperature a6-plane reflectance of six crystals over the entire frequency range.

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66 0.1 Photon Energy (eV) 1 0.1 5000 1 T 1 1 I I I I I I 1 1 1 I I I I I I 4000 Bi2212 T = 300 K Pure Y 35% Pb 50%, Y 20% "1 I I I I 1 1 1 1 I II — I I 1 1 1 1 Y123 T = 300 K Pure Pr 15% Pr 35% 1000 Frequency (cm ^) 10000 Fig. 14 The real part of the optical conductivity
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67 1 1.25 Photon Energy (eV) 2 3 0 1 T 1 1 1 1 1 1 1 Bi2212 T = 300 K 1.00 Pure Y 35% Pb 50%, Y 20% 0.75 0.50 0.25 0.00 "I I I I — I — I — I — I — I — I — I — I — I — r Y123 T = 300 K Pure Pr 15% .Pr 35% Frequency (cm ^) 30000 Fig. 15 The effective number of caxriers per plajiax Cu atom Neg{u}) obtained by the integration of ai{u}) up to a certain frequency, as described in Eq. 5.

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68 Bi2212 (Pb T, = 35 K T, = 40 K T, = 85 K 50%, Y 20%) (Y 35%) (Pure) 1 300 K 100 K " 70 K II 1 \ \ \ 1 1 1 1 0 1000 0 1000 0 1000 2000 Fig. 16 The farand mid-infraxed optical conductivity of six samples at 20, 100, and 300 K. The symbols show the dc conductivity values.

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69 Y123 Tc = 40 K T, = 75 K T, = 92 K (Pr 35%) (Pr 15%) (Pure) 2000 Frequency (cm~ ) Fig. 17 The real part of the dielectric function €1(0;) obtained by KramersKronig analysis of the reflectance data. The data shown are from u ~ 100 to 2000 cm"^ at 20, 100, and 300 K.

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70 Photon Energy (meV) 50 100 150 3000 E o T 2000 1000 200 — I 1 1 1 1 1 1 I I I I I I I I 500 1000 1500 2000 Frequency (cm~^) Fig. 18 The infrared optical conductivity for Y-doped Bi2Sr2CaCu208 {Tc = 35 K) at temperatures between 20 and 300 K. The dc conductivity values are indicated by the symbols. We also plot the results of other studied seimples.

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71 Photon Energy (meV) 50 100 150 200 3000 -1 1 1 r E o T a 2000 1000 1 1 1 r Bi221 2 500 1000 1500 Frequency (cm~^) 2000 Fig. 18-continued

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72 Photon Energy (meV) 50 100 150 200 6000 500 1000 1500 Frequency (cm~^) 2000 Fig. 18-continued

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73 Photon Energy (meV) 50 100 150 200 3000 1 1 1 r E o I G 20001 1000 I I 1 r Y1 23 -I r r 1 1 1 1 1 1 1 I I I I I I I I 500 1000 1500 2000 Frequency (cm~^) Fig. 18-continued

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74 6000 1^ 4000 O b 1 ^ 2000. Photon Energy (meV) 50 100 150 200 -T , ^ > \ 1 ' 1 \ ' > ' ' 1 ' ' ' ' \ ' ' ' ^ Y1 23 To = 75 K 300 K 200 K 150 K 100 K W 50 K ^\ 20 K Jl 1 L. 500 1000 1500 Frequency (cm~^) 2000 Fig. 18-continued

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75 6000 1^ 4000| o b 3 ^ 2000 Photon Energy (meV) 50 100 150 200 -1 1 r T Y123 1 1 1 r -I 1 L. -J I I L. 500 -J I L. 1000 1500 Frequency (cm ^) 2000 Fig. 18-continued

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76 Photon Energy (meV) 50 100 150 200 0.20 T 1 1 r -1 1 r 0.15 0.10 0.05 Bi221 2 T, = 35 K 0.00 0 300 K 200 K 150 K 100 K 75 K 20 K O 30 o o ro 4 15 * -i—T — I — I — I — r-T 250 cm 500 cm' 1000 cm 2000 cm T — I — r 1 1 . -1 . 1 -1 I I I I I I I I I v;f....' t I I t I I 1 50 100 150 200 T (K) 250 500 1000 1500 Frequency (cm~^) 2000 Fig. 19 The partial sum-rule spectrum per planar Cu atom, ^eff (w, T), for Y-doped Bi2Sr2CaCu208 {Tc = 35 K) at temperatures between 20 and 300 K. The inset shows the difFerence in ^eff (t^, T) computed in the 300 K and other lower temperatures for u; = 200, 500, 1000, and 2000 cm"!.

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77 Bi2212 Frequency (cm" ) Fig. 20 The temperature-dependent quasiparticle scattering rate 1/t{u,T) obtained from the generalized Drude model in Eq. 7 for Bi2Sr2CaCu208 and YBa2Cu307_j at severed doping levels.

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78 Fig. 21 The imaginary part of the self-energy Im E(u;, T) obtained from the marginal Fermi Uquid theory in Eq. 8 for various doping and temperatures.

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79 T, = 35 K (Pb 50%, Y 20%) 800 I — I — I — I — I — I — I — I — I — I — I — I — [" Bi2212 T, = 40 K (Y 35%) T, = 85 K (Pure) 600 -I — I I I I 1 I I I I -1 — I — I — I — I — I — I — I — I — I — r "1 — I — I — I — I — I — I — I — I — r 0 100 200 300 100^^2?°° 200 300 Tc = 40 K (Pr 35%) 800 I I — I — 1 — I — I — I — I — I — I — r T, = 75 K (Pr 15%) 1 — I — I — I — I — I — I — I — rT, = 92 K (Pure) 200 0 -I 1 1 L_I 1 I I L_L. -I 1 I I f I I T 1 1 1 1 1 1 1 1 T 0 100 200 300 100 200 300 100 200 300 Temperature (K) Fig. 22 The zero-frequency scattering rate 1/td of the Drude contribution from the two-component fit of Eq. 6 to the optical conductivity. The straight lines show a hnear fit to the temperature dependence of 1/td above Tc.

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80 Bi2212 (Frequency)"^ (cm^) (10~*) Fig. 23 The real part of the dielectric function (dashed line), plotted against w 2 at 20 K. The range of the data shown is 500-100 cm-^ The linear fits are shown by the solid lines.

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^ 81 40 Photon Energy (meV) 80 1 20 40 80 120 6000 -1 1 1 1 1 1 1 1 1 1 r Bi2212 T = 20 K 4000 Pure Y 35% Pb 50%, Y 20%, 1 1 1 1 1 1 ; 1 1 1 r 1 Y123 T = 20 K Pure Pr 15% Pr 35% 2000, — / \: ^ ^ y\ Frequency (cm ) 0 200 400 600 800 0 200 400 600 800 1000 -1 Fig. 24 The frequency-dependent superconducting penetration depth obtained from Eq. 10 at 20 K. The values of Ai(0) from the sum-rule analysis of Eq. 11 are indicated by the symbols.

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82 1 60 140 120 100 80 60 40 20 1 X 1 ' 1 BKBO 1 • La21 4(0) Bi221 2 A TI2212 / — — / V ^ 1 , 1 1 2 4 6 21 -3Fig. 25 The transition temperature as a function of ntot for Bai_^K^Bi03 (cross),"4 La2Cu04.i2 (circle),"^ BiaSraCaCuaOg (square), YBazCusOT-* (triangle), and TlzBaaCaCuzOg (diamond)."^ The solid line is a guide to the eye.

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83 Fig. 26 Tc plotted a function of n,. Cross: Bai_^Ki:Bi03,i" filled circle: La2Cu04.i2,"^ fUled square: BizSrsCaCuzOg, fiUed triangle: YBazCuaOr-tf, and filled diamond: Tl2Ba2CaCu208i^2 infrared measurements. Open circle: La2_^Sr^Cu04, open triangle YBa2Cu307-«, and open star: Tl2Ba2Cu06 from ^SR measurements."^ 120 The solid curve is the universal Ueinuraline."^ The dashed curve is based on pair-breaking model calculation. ^^0

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CHAPTER IV OPTICAL STUDY OF UNTWINNED (Bii.57Pbo.43)Sr2CaCu208+tf SINGLE CRYSTAL: AB-PLANE ANISOTROPY Introduction The dimenionality of the cuprate superconductors is an important issue, related as it is to the basic picture (Fermi liquid, non Fermi liquid, etc.) that one has for their electronic structure. It is widely accepted that the key to the high-Tg superconductors problem is hidden in the Cu02 planes, which are a common feature to all of the cuprates. Many theoretical models which attempt to explain the mechanism responsible for superconductivity are two dimensional. Thus is a reflection of the assumption that the only active pieces of the crystals are the Cu02 planes, with the rest of the material layers serving only structural or charge-balance functions. Experimentally, most einalyses, such as dc resistivity,^"^^"^"^^ the infrared conductivity^^-5^'^3'^°*'i24-i26 ^j^^ penetration depth,^^ i^^ve been performed on single-domain YBa2Cu307_i(Y123). Much of the observed anisotropy of Y123 can be attributed to the quasi-one-dimensional CuO chiiins; their presence prevents determining whether the Cu02 planes themselves have amy intrinsic properties. In contrast, Bi2Sr2CaCu208 (Bi-2212) provides a better opportimity to study the issue of the electronic structure of the Cu02 planes because there are no chains in these Bi-based compounds. A considerable investment was thought that a possible way of investigating the electronic structure of the high-Tc superconductors was to measure the size and shape of the Fermi surface. ^2*^ Recent angle-resolved photoemission spectroscopy (ARPES) is continuing to make important contributions towards understanding the electronic 84

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85 structure of the norm«il eis well as the superconducting state of the high-Tc materials. The method has been applied to map the Fermi surface of Bi-2212 completelyJ^'^^^'^-^*"^^^ Normal state spectra^'*' '^"^ show ein anisotropic in-plane Fenm surface. There is only one peak corresponding to the main planar Cu02 bcind; no resolvable Bi-layer splitting is seen above TcAll other spectral features have been attributed either to umklapp band related to the structural superlattice, or to shadow band based on the presence of antiferromagnetical spin fluctuations in the metallic state.^^^ Another important feature of Bi-2212 Fermi surface is that the observation of a large Luttinger Fermi surface containing 1 -|x holes, where x is the hole doping."^^'^^^'^^^ With decreasing temperature, ARPES is able to determine the magnitude of the superconducting gap (Ajt) on different parts of the Fermi surface. The existence of a substcintial gap anisotropy in Bi-2212 with respect to k indicates that the superconducting order parameter is not a simple s-wave.^^^'^^^'^^* Indeed, the abplane anisotropy of the superconducting gap in Bi-2212 has been confirmed by other measurements including timneling^^^ and Raman scattering. Also, the previous report by Quijada et a/.^"'^-^*^ has found that the polarized reflectance of the a6-plane of single-domain Bi-2212 crystals is cinisotropic above and below Tc. Despite these extensive spectroscopic studies, questions still exist regarding the presence of the structural superlattice, which necessarily affects the experimental data on the highest quality Bi-2212 samples. A general question arises as whether the anisotropy of aft-plane in Bi-2212 is intrinsic, or being probably due to the superstructure of the Bi-0 plane. This gives a motivation to study Pb-doped Bi-2212 single crystals since the superlattice modulation disappears (or changes) gradually as bismuth is replaced by lead:^^^ ^ structurally simplified situation and through this clarity on the influence of the modulation on the electronic structure of the Cu02 planes. In a recent ARPES study of Pb-doped Bi-2212,^'*^ it was shown that

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86 the Fermi surface still has orthorhombic symmetry. We are pursuing experimentally the measurements of the a6-plane polarized reflectance spectra above and below the superconducting transition temperature in a high quality, untwinned single crystal of (Bii.57Pbo.43)Sr2CaCu208+« [Bi(Pb)-2212]. Infrared spectroscopy is a powerful tool on the aspect of high-Tc superconductors.^"* Unlike the surfeice sensitive technique of APRES (approximately 15 A in the cuprates), infrared light probes the bulk properties of the materials. Optical methods provide information on the dynamics of the free carriers, the nature of the chcurge-transfer cind other low-energy excitations, the superconducting gap (in principal), phonons and other aspects of the electronic structure. Furthermore, using polarized reflectance measurements we have been able to obtain the optical response along the principal axes of the crystal. Interest has focused mainly on the investigation of the dielectric tensor component (avs. 6-axis) of Bi(Pb)-2212. In addition, we will compare our data on Bi(Pb)-2212 to previous optical results on Bi-2212 by Quijada et a/.^^'^-^^^ Experimental The Bi(Pb)-2212 single-crystal sample was prepared by a standard flux-growth technique. ^**'^^^ The crystal was thin platelet with smooth and uniform surface and typical dimension 2.5 x 3 x 0.2 mm^. The as-grown crystal was used without any annealing. The superconducting transition temperature was obtained by means of ac magnetization measurement. The Tc onset value for this crystal was found to be 80 K with ATc = 2 K. Characterizations of dc resistivity, ac susceptibility, Xray diffraction and low-energy electron diffraction (LEED) have been performed on similar samples grown in the same way.^'*^ The crystal structure of undoped Bi-2212 is pseudotetragonal {li/mmm I>4a space group). There is a displacive modulation of the Bi-0 sublattice along the 6-axis with a wavelength « 5 |6|^^^'"^ (taking |6| « 5.4 A). Note that in Bi-2212 structure the a and 6 axes are along the Bi-O-Bi

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87 bonds, and correspond respectively to the F-X and F-Y directions in the Brillouin zone. They axe nearly 45° from the Cu-O-Cu bond (F-M direction). By contrast, the modified modulation wavelength along the 6-axis in Bi(Pb)-2212 increases to about 13|6|, as was confirmed by LEED.^^^ The LEED pattern exhibited an almost 1x1 structure for Bi(Pb)-2212, whereas it was a 4.6 x 1 pattern for undoped Bi-2212. The change of modulation wavelength with Pb doping suggests that Pb really enters into the Bi sites. Furthermore, X-ray diffraction and LEED measurements indicate no structural change in the Cu02 planes for Bi(Pb)-2212 samples. It is worth mentioning that the recent observation by Winkeler et a/.^'*® which found that Pb doping increases the c-axis interlayer coupling in compared to the undoped Bi-2212. The out-of-plane resistivity pc{T) decreases by four orders of magnitude. The temperature behavior changes from semiconductor-like to metallic. However, it is generally believed that Pb doping does not perturb the electronic states critical to superconductivity in this system,^^^ and the electronic structure of Bi(Pb)-2212 is close to that of undoped Bi-2212. The polcirized reflectcince was measured at near-normal incidence. Far-infrcired and mid-infrared measurements were carried out on an Bruker 113v Fourier-transform infrared spectrometer using a 4.2-K bolometer detector (80-600 cm~^) and a B-doped Si photo conductor (450-4000 cm~^). Wire grid polarizers on polyethylene and AgBr were used in the farand mid-infrared, respectively. A Perkin-Elmer 16U grating spectrometer in conjunction with both thermocouple, PbS, and Si detectors was used to measure the spectra in the infrared to the ultraviolet (1000-32000 cm~^), using wire grid and dichroic polarizers. The room-temperature polarized reflectance in the visible frequency region (14300-23800 cm-^) was also made using a Zeiss MPM 800 Microscope Photometer with grating monochrometer, especially designed for spot measurements. We measured on the shiny, smooth, and well-reflecting spots with

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88 a size about 50 x 50 /im^ by using a magnification of 10 x and 20 x. For lowtemperature measurements, the sample was mounted in a continuous flow helium cryostat equipped with a thermometer ajud heater near the cryostat tip, regulated by a temperature controller. Calibration of the absolute vaJue of the reflectance was done by coating the scimple with a 2000 A film of Al after measuring the uncoated sample. The spectra of the uncoated sample were then divided by the obteiined spectrum of the coated sample and corrected for the known reflectance of Al. The accuracy in the absolute reflectance is estimated to be ±1%. However, the accuracy of the anisotropy of the reflectjoice (i.e., the difference between a and 6 results on the same sample at the same temperature) is better than ± 0.25%. The optical properties (t.e., the complex conductivity
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89 Results and Discussion Polarized reflectance In Fig. 27 we show the room-temperature polarized reflectance of Bi(Pb)-2212 and Bi-2212*^^'^^^ (inset) crystals measured over a wide frequency range. Surprisingly, the anisotropy features of the spectra of Bi(Pb)-2212 and Bi-2212 are cdmost the same. The a-axis reflectance is higher than the 6-axis reflectcince by 1-2% in the far-infrared region. As the frequency increases, the reflectance falls off in both polarizations. The position of the plasma edge for the 6-cixis poleirization occurs at slightly lower frequency than in the a-eixis direction. The splitting is estimated to be around 500 cm"^ in contrast to the studies,^^'^^'^''^°^'^24-l26 untwinned Y123, which showed a significant difference (~ 5500 cm~^) in the a and b axis plasma edge. The larger plasma edge along the b direction in the Y123 system heis been attributed to the presence of CuO chains along the b axis. However, neither Bi-based compounds has chains, indicating that the electronic excitations within either the Cu02 or Bi-0 planes being themselves anisotropic. Our residts for Bi(Pb)-2212 favor the anisotropy introduced by the Cu02 planes since the displacement modulation ailong the 6 axis is partly suppressed by substitution Pb for Bi. We have also foimd that for both samples the reflectance is substantially higher in the b axis above the plasma minimum. In addition, there axe two electronic absorption bands at ~ 2.3 and 3.8 eV in both polarizations. There is general agreement that the broad band at ~2.3 eV is associated with 0 2p ^ Cu 3d charge-transfer excitations in the Cu02 plane. But identification of the ~3.8 eV excitation remains controversial. So far, there are two possible candidates for the origin of this band. One is the optical transition within the Bi202 layers, e.^r., between Bi 6p and 0 2p, and the other in the Cu02 layers. Of course, it is possible that both excitations overlap with each other. As seen in the inset of Fig. 27 for the Bi-2212, the absorption band at ~ 3.8 eV is more pronoimced along b than in the a direction. The difference is smaller in Bi(Pb)-2212.

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90 Naturally, it would be preferable to think that the 3.8 eV peak could be associated with transitions occurring in the Bi-0 layers because of the substitution of Pb in Bi2212 having a strong influence on the incommensurate modulation along the 6 axis. However, the discrepancy may cdso arise from the difference in the oxygen doping level of samples. At the moment our optical data is not enough to distinguish such electronic transitions from each other. One could question whether the anisotropy in polarized reflectance spectra is inhomogeneity of high-Tc samples parallel to the c axis. Such inhomogeneity could result in surface steps with different structure or composition. We regard such effects as extremely imlikely in the present study. In all, the Bi(Pb)-2212 and Bi-2212 crystals are grown by different groups. We have examined on shiny, smooth and wellreflecting siuiaces in all measurements. The high degree of anisotropic reproducibility in visible frequency region was also obtained by using Microscope measurements. On the other hand, we must note that similar polarization dependence has been seen in earlier ellipsometric measurements on Bi-2212,^^* with a transition at ~3.8 eV stronger and sharper for electric field polarized along the modulation direction. The a6-plane anisotropy has also been observed in the fax-infrared transmittance of free standing Bi-2212 single crystals. Considering all of the above, we believe that the observed anisotropic behavior is an intrinsic property of these Bi-based cuprates. Optical conductivity The Kramers-Kronig transformation of the polarized reflectance data of Bi(Pb)2212 yields the real part of the conductivity ai(a;) shown in Fig. 28 for several temperatures. Essentially, the spectra are similar to Bi-2212.^°'^'^*l In all cases, as T is lowered from room temperate to just above Tc, we observe a sharpening and an increase of the far-infrared conductivity, on account of the increasing dc conductivity. At higher frequencies, (ti{u) does not show much temperature-dependent variation.

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91 In addition, the normal-state cri{u) has a frequency dependence that decays much more slowly than the uj~'^ expected for a material having a Drude response. This non-Drude behavior, which is universal in the optical conductivity of the copper-oxide superconductors, has been the subject of considerable discussion and controversy.^"* Upon entering into the superconducting state, the far-infrared conductivity falls rapidly to a value well below the normal-state value. The area (spectral weight) below Tc is smaller than that above Tc. The missing-area below Tc is a effect of the condensation of the free Ccirriers that are responsible for the normal-state transport into the superconducting pciirs. The spectral weight imder the ) curve is removed &om the finite frequencies and shifted into a S fimction at a; = 0. The residual low-lying conductivity remains even at T «C Tc. One possible origin of this is the low-frequency tail of the non-Drude component and other high frequency interband transitions. The other cause could be thermally excited quasiparticle infrared absorption associated with node(zeroes) of the gap function on the Fermi surface. There is also a kneelike structure developing in the superconducting state (Ti(u) at a; ~ 500 cm~^ It was shown by Reedyk et al.^^ that similar structure may occur due to interaction of cin electron continutmi with c axis LO phonons.^^ As shown in Fig. 28, the einisotropy in the normal state conductivity is about 10%, with the far-infrared conductivity higher in the a direction and the high-frequency conductivity is higher along b. Below Tc there is a definite anisotropy to the iaiinfrared conductivity, with a considerably larger conductivity along the b axis down to ~ 20 meV. The anisotropic behavior of optical conductivity in Bi(Pb)-2212 is very similar to 31-2212.^°^'^*^ However, there are important differences in the vibrational structures of
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92 655 cm~^ . The splitting of vibrational line at low temperature is probably due to the haxis superlattice structure. In Bi(Pb)-2212, the 640 cm~^ phonon mode is visible along the a and b axes, but stronger in the b direction in the whole measured temperature range, which led us to believe that Bi(Pb)-2212 is less structurally anisotropic. Thus, it is reasonable to speculate that the observed aft-plane «inisotropy of Bi(Pb)-2212 is attributed to the anisotropy of electronic structure within the Cu02 plane, rather than the structural superlattice in the Bi-0 layer. Oscillator strength sum rule In view of the fact that the aft-plane cinisotropic conductivity of Bi(Pb)-2212 shown in Fig. 28, it is important to quantify the spectral weight by integrating the optical conductivity from zero to a certain frequency hu. Based on the conductivity data, we define the partiail sum rule, (m/m*)iVeff(u;) as^° where m* is the effective mass of the Ccirriers, m is the free-electron mciss, Vcf.\[ is the unit cell volume, and iVcu is the number of CuO layers per imit cell. Here, we use iVcn = 2 for Bi(Pb)-2212. {m/m*)Ncf[{u}) is proportional to the nimiber of carriers involved in optical excitations up to hui. In Fig. 29 we plot the room-temperature results for (m/m*)iVeff(a;) per planar Cu atom along a and ft axes. The inset shows the diflFerence between {m/m*)Ncg{u}) for the two polarizations. First, (m/m*)iVeff(w) shares a common feature jJong both directions: It rises rapidly at low frequencies due to a Drude-like band peaked at a; = 0, and begins to level off near 8000 cm"\ then rises again above the onset of the charge-transfer band. Second, the difference between (m/m*)iVeff(u;) for the two polarizations shows that there is more spectral weight (w < 5000 cm~^) in the (12) 0

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93 a direction. With increcising frequency, two (m/m*)iVejf (w) curves come together around 8000 cm~^ Differences appeai again at higher energies; in particulzir the baxis value is higher thcin the a axis value. One cein also see from the inset of Fig. 29 that the difference of effective carriers number between two polarizations is small below 8000 cm~^, but becoming laxger at higher frequencies. Dielectric function models One crucial question about the analysis of our measurements is whether the anisotropy is due to anisotropy of electronic structure (i.e., effective carrier concentration or effective mass) or to anisotropy of scattering rate. Two approaches are usually considered in interpreting infrared data from superconducting cuprates. The first takes there to be two sets of charge carriers, a Drude contribution centered at w = 0 and a second mid-infrared absorption band axising from bound charges such ) describe the frequency-dependent (imrenormalized) carrier scattering rate and mass enhjincement so that the effective mass is given by m*(u;) = m(l + A(a;)). Note that 1/T(a;) and A(u;) obey KramersKronig relation. A frequency-dependent scattering rate also arises in the models that provide a phonomenological justification for this one-component approach including the

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94 marginal Fermi liquid (MFL) theory of Varma et a/.,*^'*^ and the nested Fermi Uquid (NFL) theory of Virosztek et al.^^'^^ In these models, the dielectric ftmction is = u,[u; 2S(a;/2)] ^^^^ with the self-energy of the charge carriers (essentizJly the scattering rate) taking the form, ( w^XtT, u}
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95 1/t{u),T) = 1/to + 1/t(u;) + 1/t{T), where the first term stands for the impurity scattering, the second and third terms for the u and T dependence, respectively. We taJce difference between 1/t{uj,T) for the a and b polarizations. It is found that the enhanced scattering rate along the 6 axis could be mainly attributed to tin increase of 1/to by 200-300 cm~^, while the frequencyand temperature-dependent contribution is small. It should be noted that some similcirities of the scattering rate along a and b axes are evident. At room temperature, the spectrum increases with frequency in nearly linear fashion. With decreasing temperature, the scattering rate remains linear and shows a simple temperature-dependent decrease. Interestingly, as temperature is reduced to 100 K, the scattering rate is suppressed below 800 cm~^ while the highfrequency part of 1/t{uj,T) still remains linear. In the superconducting state, the low-frequency 1/t{u),T) is depressed significantly. The suppression in 1/t{u),T) at low frequencies a.t T > Tc has been pointed out previously and discussed in relevance to a pseudogap state.^^"*^ With regcirds to the frequencyand temperature-dependent behavior of the scattering rate,''^~^° our Bi(Pb)-2212 sample with Tc = 79 K may be viewed as a lightly overdoped cuprate. For comparison, we also applied the MFL analysis to the a6-plcine optical conductivity. Figures 31 and 32 show the imaginary part of the self energy Im S(a;, T) and effective mass enhancement m*{u))/m of Bi(Pb)-2212 at several temperatures and along a and b axes. The MFL analysis in Fig. 31 has two interesting results. First, for two polarizations the frequency-dependent imaginary part of the self-energy has a linear-in-u; dependence up to frequency of 1000 cm~^ Second, the -ImE(ci;,r) is different between the a and 6 axes. The &-axis Im T,(u}, T) increases constantly for about 100-150 cm~^ Moreover, we estimate the slope of -ImS{w,r) between 200 cm-^ and 1000 cm"^ at 300 K, which yields a coupling constant 0.28 and

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96 A* ~ 0.30. This result suggests that the coupling between the charge carriers and whatever excitation which dominates the linear scattering rate has tensor components. While these characteristic numbers are larger at 100 K, i.e., 0.37, 0.39. The temperature dependence in A,,, clearly shows that the coupling mechanism that is causing the linear scattering rate in the charged carriers becomes stronger as the temperature of the sample is decreased. Similar behavior has also been reported in same analyses of unpolarized measurements of Bi-2212 by Romero et aO^^ As expected for the MFL picture, the effective mass, shown in Fig. 32, is enhcinced at low frequencies, and then drops off to equal the bcire electron mass at high frequencies. This also means that axL increcise of m*[uj)/m results in a decre«ise of — Im S(a;, T) at low frequencies shown in Fig. 31 since heavy carriers tire more difficult to scatter. It is clearly discernible that the mass enhancement at low frequencies is slightly anisotropic in the airplane, on account of the small difference in the VcJues of Up. At room temperature the extrapolated [m*{u) = 0)/m] ~ 2 is comparable to those obtained from m* ~ 2m for the direction F-X of Bi-2212 by the density functional method. The temperature-dependent chcinge of the effective mass is enhanced at lower frequencies by an amoimt which is largest at lower temperatures. Two component picture . We now turn our attention to the two-component approach which has been widely used in anjilyses of the a6-plane optical conductivity in highTc superconductors. In this model, the free carriers are assumed to account for the dc conductivity and far-infrared, T-dependent part of the spectnma while the mid-infrared part accounts for the non-Drude part. The free-carrier component was fit to a Drude model. The mid-infrared and high-energy components were fit by Lorentzian oscillators. The dielectric function is = 2/-^/ + Yl —2 -P—+ «oo, (16)

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97 In Eq. 16, the first term represents the Drude component described by a plasma frequency Upj) and scattering rate l/r/j; the second term is a sum of midinfrared and interband oscillators with oJj, u>pj, and 7^ being the resoneint frequency, oscillator strength, and the width of the j*^ Lorentz oscillator respectively. The last term, Cqo, is the high frequency limit of c(u;), which includes higher interband transitions. The two-component analysis is in accord with two expectations. First, the fitting results indicate that the oscillator strength for the Drude term is nearly temperatiire independent. We find w^^ = 9000 ± 200 cm"^ and wj^ = 8600 ± 200 cm'^ When T > Tc, the scattering rate of the free Ccirrier or Drude contribution has a linear temperature dependence, shown in Fig. 33. Such a Tlinear behavior in 1/t£> above Tc has been observed previously by infrared measurements^^'^^'^"^ and is a unique property of the cuprate superconductors. Below Tc, the scattering rate 1/tj) exhibits a fast drop, suggesting a strong suppression of the scattering channel at the superconducting transition. It is remarkable, moreover, that the fitted 1/td is anisotropic and the 1/tj) obtained for the b axis is larger than the one obtained for the a axis at each temperature. Writing K/td = 27rX[) ksT -f ^/ro,^°^ a straight line fit to the 1/t£) above Tc yields the coupling constant as ~ 0.29 and A^, ~ 0.30. This indeed is a week coupling vcilue. The observed anisotropy of the 1/t£) for Bi(Pb)-2212 could be connected with the transport anisotropy in the normal state. Using the parzimeters of Drude plasma frequency given above and the temperature dependence of 1/t£>, the dc resistivity may be written as {p„ = (Wp£)r£>/60)~\ in units of fi-cm), and is shown in the inset of Fig. 33. Two transport data (averaged a&-plane) obtained for crystals similar to ours have also been included.^^^ It is found that the dc resistivity anisotropy in the a6-plane of Bi(Pb)-2212, /jf,//)? , is 1.15-1.22. This behavior shows once again that the anisotropy in the dc resistivity for Bi(Pb)-2212 is caused by the anisotropy of the free-

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98 carrier relaxation rate combined with the normaJ-state anisotropy of the Drude plasma frequency. In addition, the transport measurements performed on similar samples shows the absolute value of averaged afe-plane dc resistivity is increased by a factor of as much as 1.8 compared to our results deduced from the optical measurements. The discrepancy may arise from the differences in oxygen stoichiometry. To our knowledge, there have been no reports on the anisotropy in the a6-plcine dc resistivity of Bi(Pb)2212, and we are preparing to make these measurements in our lab. However, the close agreement in the anisotropy of the dc resistivity deduced from the optical and transport measuremnts hcis been previously observed on Bi-2212.^*^ Superconducting state Anisotropy of the ab — plcine . As was stated previously, there is definite anisotropy of the fcir-infreired conductivity in the superconducting state, shown in Fig. 28. The fr-axis conductivity is larger thcin the a-tixis conductivity at 50 and 10 K. The exact value of the observed superconducting-state cinisotropy is difficult to quantify partly because the a6-plane infrared reflectivity is close to unity below Tc and thus high accuracy is required to detect any small anisotropy. Nevertheless, concerning this low-frequency anisotropy in (tI{u) and cr\{ijj) below Tc, two possibilities are considered at present. First, in the one-component picture, the superconducting-state conductivity is due to excitations across the superconducting gap. Hence, the gap must be anisotropic. It has been shown by ARPES, that the superconducting gap, at least in Bi-2212, is highly anisotropic in ifc-spcice.^^^'^^^'^^* If this interpretation is adopted, the differences between the a and 6 directions of optical conductivity for Bi(Pb)-2212 in the superconducting state would imply a two-fold symmetry to the superconducting gap absorption. Then, our data is contradictory to most of the experimental results for Bi-2212 mentioned above. It is generally concluded that there is a large gap anisotropy in Bi-2212 which closely mimics the four-fold symmetry of a

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99 dj.2_y2 superconducting order parameter. ' Here, we would like to point out that a two-fold axis of symmetry in Bi(Pb)-2212 does not originate from a change in the periodicity of the superlattice modulation since the similar superconductingstate anisotropy of the optical conductivity has been reported in 61-2212.^"^'^^^ The second possibility is that with the choice of the two-component picture, the observed iinisotropy in (100/ir) = 250 cm~^ for the h axis eind 220 cm~^ for the a axis). Above and below Tc, the second mid-infrared component has a larger contribution along the h axis than along the a axis. This anisotropy points to a definite anisotropy of the electronic structure within the ai^-plane. Superconducting condensate . Although the measured optical data does not by itself distinguish between the above two possibilities, the a6-plane anisotropy of the amount of conductivity that condenses into the 6 fimction at u; = 0 is given less ambiguously from the missing tirea of the optical conductivity spectrum in the superconducting state. The missing area Cein be written in terms of the plasma frequency of superconducting carriers, uJpSi by sum-rule cirgument: 2 °° ^ = y" (^in(u;) cri,(a;))du; (17) 0 where (Tin(a>) and p5 is related to superfluid density, n,, by ijjps = \/47rn,e2/m*, and also to the superconducting penetration depth, A^, by \i c/ups where c is the light speed. Evaluation of the integral in Eq. 17, we obtain the values of u)^g = 8600 ± 200 cm"^ and wj^ = 8150 ± 200 cm"^ in Bi(Pb)-2212 at 10 K. The results indicate the superconducting carrier response is larger along the a axis.

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100 The afe-plane anisotropy of superfluid density mirrors the einisotropy of the superconducting penetration depth. In Fig. 34, we plot the frequency dependent penetration depth of Bi(Pb)-2212 along a and b axes at 10 K. This quantity is defined as c2 47ra;(T2(a;) 1/2 (18) where ) is the imaginary part of the optical conductivity obtained from KramersKronig aucdysis of the reflectance data. Note that a smaller Xi woxild correspond to a Icirger superfluid density. The fact that both curves in Fig. 34 are nearly flat suggests that the primary contribution to (T2{uj) is from the superfluid carrier response. The extrapolated zero-frequency penetration depth approaches the values given by sumrule analysis (symbols at a; = 0 in Fig. 34), i.e., ~ 1850 A and ~ 1950 A. In addition, the values of AJ and A^ for Bi(Pb)-22212 are very close to those for Bi-2212,1^^ A^ ~ 1800 A and AJ, ~ 1960 A. While the anisotropy ratio, A^/AJ ~ 1.05, for Bi(Pb)-2212 is smaller than that, X''JXI ~ 1.1, for Bi-2212. Spectral weight above and below Tq . We now turn to a comparison among the various contributions to cri{u}), above and below Tg. We have used finite-frequency sum-rule analysis in Eq. 12 and then calculated the effective number of carriers per planar Cu atom in the low frequency region below the chargetransfer gap (u; < 16000 cm ) as iVitot, the Drude or free carrier part (from two-component analysis) as ^Drndo and the superconducting condensate weight as Ng. At present we have taken the effective mass to be the free-electron mass. Results for Bi(Pb)-2212 and Bi-2212^°^'^*^ are sunomarized in Table 5. We first describe the results of iVtot and will discuss others latter. For a comparison, we note that the values of N^^^ and N^^^ for Bi(Pb)-2212 are slightly higher than those for Bi-2212, although iV* t is always larger than N^^ in both materials. The slight increase of the total carrier numbers for Bi(Pb)-2212 may be related to the Pb content or the oxygen stoichiometry. The

PAGE 109

101 diiferences of the a-axis and 6-eixis contributions to iVtot reflect that the total &-cLxis conductivity below the chargetransfer baud contains more spectral weight than that in the a direction. The anisotropy ratio iVtotZ-^tot ~ 1-05 of Bi(Pb)-2212 coincides with the value obt«dned by Bi-2212. This is remarkable: as the substitution of Pb in Bi-2212 induces a new inconunensurate modulation periodicity in the b direction, but does not make a significant change on the anisotropy ratio of the total carriers number (6vs. a-axis) compeired with that in Bi-2212. Therefore, it appears that the origin of the afe-plane cinisotropy in Bi(Pb)-2212 is the same as in Bi-2212. Our data provide evidence that within the Cu02 plane the electronic properties of these Bi-based compounds are anisotropic, regardless of the superstructure in the Bi-0 layer. Table 5. Effective nimiber of carriers per planeir Cu atom. Material ^|| N^ot iVorude #-% (Bii.57Pbo.43)Sr2CaCu208+« a 0.40 0.103 0.093 23 90 b 0.42 0.094 0.084 20 89 Bi2Sr2CaCu208 a 0.37 0.105 0.094 25 90 b 0.39 0.096 0.083 21 86 Typical uncertciinties ±.03 ±.01 ±.01 ±1% ±4% It is important to discuss one relation between optical properties eind the Fermi surface. In simple metals, the voltmie enclosed by the Fermi surface corresponds to the total ntmaber of carriers. The carrier concentration iVtot can be related in terms of the area Sf the Fermi surface would have: A^tot > ^2^' ^^^^^ is the Fermi wave vector and the equality holds if the Fermi surface is spherical. Here, we should also remark that cuprates eire not simple metals, and there is strong experimental

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102 evidence to show that cuprates have a cylindrical shape Fermi stirface.^"^* Moreover, the optical properties are generally quite complicated and one cjumot expect to be able simply to use optical measurements to study the Fermi surface. But what is important here is the ideas involved, to see that, at least in principle, there is a correlation between optical properties and Fermi surfaces, and that the correlation is conceptually quite simple in limiting cases. Thus, for Bi(Pb)-2212 and Bi2212 in which the N^g^ is always larger than N^Q^ would imply Sp > Sp. The b polarization of the Fermi surface is weighted more heavily thcin a. This result suggests that the Fermi surface is anisotropic between the a and 6 axes. Our simple assumption is in agreement with the ARPES results, which find that the Fermi surfaces of Bi(Pb)2212 and Bi-2212 exhibit orthorhombic synametry, i.e., F-X and F-Y are inequivalent in the Brillouin zone.'^^'^^^ Finally, we would like to point out that the a6-plane anisotropy of the Fermi surface for Bi(Pb)-2212 and Bi-2212 seems unlikely to be due to the observed change in interlayer coupling.'^* As previously mentioned, Pb doping reduces the normal-state resistivity anisotropy ratio, pdPahi by severed orders of magnitude compared to the undoped Bi-2212.^'*^ In contrast to this, the spectral weight ratio of the a6-plane conductivity for Bi(Pb)-2212 is identical to that for Bi2212, irrespective of its dimensionality. We examine the number of effective carriers in the Drude part and the superfluid per copper displayed in Table 5. The value of A^o^jg is smaller than ATg^^^^ (the opposite is the case in the total carriers nimaber), and the anisotropic ratio ^^DrndeZ-^Drnde is ~ 1.1. In the superconducting state, the anisotropy ratio N^IN^ is about 1.1, which is almost the same as the anisotropy of the effective nimiber of the free carriers. It is interesting to note that the nimaber of free carriers and the number of superconducting carriers are both larger for polarization along a than along 6. We also consider the superconducting condensate fraction in Table 5. In

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103 the Ccise of Bi(Pb)-2212, the superfluid density consumes about 20-25% of the total doping-induced oscillator strength, as revealed by the conductivity in both the a and b polarizations in Fig. 28. About 75-80% remaining conductivity can be observed in the superconducting state for both polarizations. If the two-component picture is adopted, nearly 90% of free-carrier spectral weight condenses to form the superfluid density cilong the a and 6 axes. These numbers are consistent with the basic cle
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104 Furthermore, both the one-component and two-component analyses have been employed to the a6-plane opticcd data. The overall magnitude of the low-frequency scattering rate and effective mass enhancement, regardless of temperature dependence, is larger along b than those along a. This indicates the normal-state infr tired anisotropy of Bi(Pb)-2212 originates not only from the mass anisotropy, but also from the scattering rate anisotropy. As a consequence, our results provide evidence that within the Cu02 plane the electronic structures of these Bi-based cuprate superconductors are anisotropic. The a6-plcLne anisotropy observed in the normal-state conductivity of Bi(Pb)2212 persists in the superconducting state as well. Below Tc, there is a definite anisotropy to the far-infrared conductivity, with a considerably larger conductivity along the b axis down to ~ 20 meV. This anisotropy could be due either to anisotropy of the superconducting gap or to anisotropy of the mid-infrared component to the conductivity. Another important finding is that the superfluid response is larger along a than 6, corresponding to values of the superconducting penetration depth, XI ~ 1850 A and AJ, ~ 1950 A. The oscillator strength of the superfluid contains about 20-25% of the total-doping induced carriers or near 90% of the free-carrier spectral weight in the normal state. This suggests the clean-limit picture resides on the a and 6 polarizations of Bi(Pb)-2212.

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105 Photon Energy (eV) 0 12 3 0 10000 20000 30000 Frequency (cm ) Fig. 27 The room-temperature reflectance of (Bii.57Pbo.43)Sr2CaCu208+; over the entire frequency range for light polarized along the a and 6 axes. For comparison, inset shows the 300K polarized reflectance of BizSrzCaCuzOg.^"

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106 Photon Energy (meV) 0 50 100 150 200 0 50 100 150 200 0 500 1000 1500 0 500 1000 1500 2000 Frequency (cm~^) Fig. 28 Left panel: Temperature dependence of the a-axis optical conductivity obtained from KramersKronig analysis of the reflectance spectra of (Bii.57Pbo.43)Sr2CaCu208+i. Right panel: Results for the b axis.

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107 Photon Energy (eV) 0.0 0.5 1.0 1.5 2.0 Fig. 29 The room-temperature effective number of carriers per planar Cu atom for polarization along a and h axes of (Bii.57Pbo.43)Sr2CaCu208+«, obtained from an integration of the conductivity using Eq. 12. The inset show the difference of effective carrier numbers between two polarizations.

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108 Photon Energy (meV) Frequency (cm ) Fig. 30 The temperature-dependent quasipaxticle scattering rate l/T{iJ,T) obtained from the generalized Drude model in Eq. 13 for (Bii.57Pbo.43)Sr2CaCu208+, along a aind b axes.

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109 Photon Energy (meV) 0 50 100 150 200 0 50 100 150 200 0 500 1000 1500 0 500 1000 1500 2000 Frequency (cm~^) Fig. 31 The imaginary part of the self-energy -ImS(a;,r) for (Bii.57Pbo.43)Sr2CaCu208+« obtained from the marginal Fermi liquid theory in Eq. 14 at several temperatures and two polarizations.

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110 Photon Energy (meV) 0 50 100 150 200 0 50 100 150 200 Frequency (cm~ ) Fig. 32 The frequency-dependent effective mass m*(a;)/m at various temperatures for (Bii.57Pbo.43)Sr2CaCu208+«.

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Ill Fig. 33 The zero-frequency scattering rate l/r/, (symbols) of the free carrier contribution from the two-component fit of Eq. 16 to the optical conductivity of (Bii.57Pbo.43)Sr2CaCu208+«. The straight Une shows a linear fit to the temperature dependence of I/td above Tc. The inset shows the afr-plane anisotropy of the dc resistivity (symbols) deduced from the optical measurements and the averaged afr-plane dc transport data (dashed line) of similar samples obtained by Ma et al}^^

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112 3000 2500 o< 2000 1500 1000 Photon Energy (meV) 20 40 60 80 Bi(Pb)-221 2 T = 10 K a axis b axis 0 100 200 300 400 500 600 -1 Frequency (cm ) 700 800 Fig. 34 The aft-plane frequency-dependent superconducting penetration depth Az(u;) of (Bii.57Pbo.43)Sr2CaCu208+i at 10 K, obtained from Eq. 18. The values of \l(0) from the sum-rule analysis of Eq. 17 are indicated by the symbols.

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CHAPTER V AB-PLANE OPTICAL SPECTRA OF IODINE-INTERCALATED Bii.gPbo.i Sr2CaCu2 Og+tf : NORMAL AND SUPERCONDUCTING PROPERTIES Introduction It is generally considered that the layered crystal structure of high-Tc superconductors is responsible for their extremely anisotropic behavior, making the physical properties of the cuprate superconductors remaxkably anisotropic.^^ For example, one striking feature of these high-Tc materials is their electrical transport anisotropy. The normal-state in-plane resistivity typically varies linearly with temperature, whereas the out-of-plane resistivity almost universally displays semiconducting behavior.^^^ In the case of Bi2Sr2CaCu208 (Bi-2212), the ratio of the out-of-plane to in-plane resistivities pc/pab can be as high as 10^. This transport anisotropy^^^ is derived from the structured anisotropy. A common view is that the quasi-two-dimensional Cu02 pleines of the cuprate superconductors mednly control the electronic conduction and are intimately related to the superconductivity. In contrast, the influence of the interlayer coupling within the Cu02 planes on the physiceJ properties is not yet well understood, although some important models depend on it.^^^"^^'' Previously, it was reported that iodine can be intercalated between the double Bi-0 bilayer of Bi-2212 (IBi-2212) and therefore tune the interlayer coupling strength.^^^"^^* Structural studies*^^"^^^ of this material reveal that the iodine intercalation expands the c-axis tmit-cell dimension in Bi-2212, whereas it has little effect on the in-plane a and b parameters. In terms of transport, the net effect of iodine intercalation is to depress the superconducting transition temperature Tc by about 10 K. Moreover, the temperature dependence of the resistivity along the c axis changes 113

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114 from a semiconducting form to a metallic-like behavior. A general question hcis raised to whether the decrease of Tc through the intercalation depends on changes in doped carrier concentration, or is due to a reduced coupling between the superconducting Cu02 layers. Early reports^^^"^^'* have considered charge trfinsfer associated with the intercalation of iodine to be negligible effect compared to the change in coupling between the layers. By contrast, an increase in hole density for IBi-2212 was suggested by measurements of Hall effect and X-ray photoemission spectroscopy (XPS).^^^'^^^ Thus, it hcis been concluded that the observed changes in Tc is caused by the charge transfer from the iodine to the Cu02 planes. Further, from the pressure dependence of the Hall coefficient^^^ of IBi-2212, the hole concentration appears to be situated in the overdoped region of the general Tc vs. hole-concentration phase diagreim. Recently, an angle-resolved ultraviolet photoemission spectroscopy (ARUPS) study^^* of IBi-2212 and O2 amnealed Bi-2212 found that Tc is significantly affected by interlayer coupling effect rather than solely by hole doping to the Cu02 planes. Fujiwara et al}^^ and Kluge et al}^^ have also investigated the effects of iodine intercalation for Yand Co-substituted Bi-2212, respectively. Based on the resistivity and ac susceptibility measurements, it was claimed that Tc evolution upon intercalation is likely dependent on both factors: the doped hole concentration and interlayer coupling. Another question of interest is the valence state of iodine in IBi-2212. The XPS studies ^^^'^^^ show that the iodine is Icirgely in a strongly ionized I~ form but with a small proportion occurring as I^+. According to the pressure dependence of Hall effect measurements^^^, the valence state of iodine in IBi-2212 is I3 molecular anion state. At high pressure, the I3 anion probably decomposes as follows: I3 — »• 31 -|2p (p is a hole). A Ramcin study of IBi-2212^^^ edso confirms the guest iodine is stabilized as a anion, acting as «in electron acceptor. Another Raman measurement has detected the presence of polyiodides (I^ and possibly I^) in the host lattice. On the

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115 contrary, a Raxaan-scattering experiment has been interpreted to imply that the intercalated iodine atoms aire not ionized and exit as I2 molecules. In this chapter, we report the a6-plane reflectance spectra of an IBi-2212 single crystal in the frequency rcinge from the far-infrared to the near ultraviolet, at temperatures above and below Tc. Infrared spectroscopy measurements have been proven to be a powerful cinalysis technique for chciracterization of high-Tg superconductors."^"* Our goal is to determine how the iodine intercalation affects the a&-plane optical response of Bi-2212. The results presented here are compared with data for the pristine Bi-2212^^'^°^'**^ to show the change of optical properties after the iodine intercalation. On the basis of the optical data, we will also discuss the origin of the decrease in Tc through intercalation and the Vcilence state of intercalated iodine atoms. Experimental Single-crystal IBi-2212 was prepared using the method reported by Xiang et 161-164 jjjg nominal composition of our host crystal was Bii.9Pbo.iSr2CaCu208+«. For the most part, such a small amount of Pb doping does not affect the crystal structure of Bi-2212 itself, but does affect on the superlattice periodicity along the b axis. The dimensions of the sample were about 2 X 2 X 0.1 mm'. The superconducting transition temperature Tc was determined by ac-susceptibility measurements on the same sample used in the optical study. The Tc onset is 80 K with ATg = 4 K, so we take the midpoint as Tc = 78 K. Characterizations of dc resistivity. X-ray diffraction, low-energy electron diffraction (LEED), XPS, and ARUPS have also bee performed on similar samples. The optical reflectance spectra of IBi-2212 were measured for light polarized parallel to the at-plane from 80-40000 cm"* (10 meV-5 eV), and at temperatures between 10 and 300 K. A Bniker IFS 113v Fourier transform spectrometer was used in the far-infrared and mid-infrared regions (80-4000 cm"^), while the near-infrared to near

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116 ultraviolet regions (1000-40000 cm-^) were covered using a PerkinElmer 16U grating spectrometer. Temperature measurements in the whole frequency range were made by using a continuous helium flow cryostat with a ctilibrated Si-diode thermometer. The 300-K absolute reflectance was calibrated by the data measured with a Zeiss Microscope Photometer system in the range from 5000 to 40000 cm~^ Moreover, all the spectra are also normalized to the same sample coated by a 2000A thick layer of Al to correct the surface scattering loss. Due to the wide frequency range of our measurements, the optical constants can be estimated by KramersKronig analysis of the reflectance data.^'' Formally, the Kramers-Kronig transformation requires a knowledge of the reflectance spectra at all frequencies from 0 to oo, and so one needs to extrapolate the reflectance data to energies which the measurements do not cover. At low frequencies the extension was done by modeling the reflectance using the Drude-Lorentz model and using the fitted results to extend the reflectance below the lowest frequency measured in the experiment. Between the highest-frequency data point and 40 eV, the reflectance was merged with the Bi-2212 results of Terasaki et al}^^; beyond this frequency range a free-electron-like behavior of u}~^ Weis used. Results and Discussion Relfectance spectrum Figure 35 shows the afr-plane reflectance of IBi-2212 at several temperatures over the entire measured frequency range. We begin with the room temperature results. In the infrared region, the reflectance value of IBi-2212 is over 80% for u < 1000 cm~^ at 300 K. As the frequency increases, the reflectance falls off. At higher frequencies, we observe a plasma edge, with a minimum at u; ~ 8500 cm~^ For frequencies above the plasma minimum, there are several characteristic band of peaks between 10000

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117 and 35000 cin~^ Some of these transitions come from the iodine contributions; there are more clearly seen in the conductivity spectrum discussed later. The inset of Fig. 35 compares the 300-K reflectance spectnmi of IBi-2212 and Bi-2212.^°^'^*^ Three important differences between the spectra. First, at low frequencies the reflectance of IBi-2212 is slightly lower than that for Bi-2212, Second, the plasma edge for IBi-2212 occurs at lower frequency than Bi-2212. Third, we find the reflectcince is substantially higher for IBi-2212 at frequencies above the plasma minimum. Three new interband transitions of IBi-2212 are evident in this frequency region. One is seen aroimd 17000 cm~\ the second around 23000 cm~^, and the last one is at ~ 34000 cm~^. As discussed below, these peaJcs are associated with the iodine atoms. When the sample is cooled, there is a substantial temperature dependence in the reflecteince up to mid-infrared frequencies, which increases quickly with decreasing temperature until 45 K; changes with temperature below 45 K are much less prominent. At low temperatures, weak phonon modes are also visible in the infrcired region. In addition, we observe below Tc the chciracteristic shoulder in the reflectance at ~ 500 cm~^ which is a common feature of many cuprate superconductors.^^ The temperature dependent behavior shows the opposite behavior at high frequencies. There is a gradual sharpening and steepening of the plasma edge as the temperature of the sample is lowered. At the same time, the reflectance is reduced (sample becomes less reflecting) for frequencies in the visible and above. Optical conductivitv The real part of the optical conductivity, a\{u), calculated from Kramers-Kronig analysis of the reflectance curves in Fig. 35, is presented in Fig. 36. The temperature dependence of the reflectance gives corresponding changes in
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118 lowered. The low-frequency conductivity then decreases dreimaticaUy below Tc. The difference in area between the normal-state and superconducting-state conductivities is associated with the condensation of the free carriers into the superfluid. The conductivity has a modest temperature dependence at mid-infrared frequencies. The mid-infrared conductivity is reduced when cooling the sample from room temperature down to 10 K. We also find that the high-frequency conductivity (a; > 10000 cm"*) gradually decreases with decreasing temperature. As mentioned previously, all the phonon modes and the electronic bands that were seen in the reflectance axe more easily resolved in the (7i{u) spectrum. We observe weeik phonon resonances at 10 K, most notably at ~ 147, 200, 440, 620, and 670 cm~\ indicated by the arrows in Fig. 36. Any other possible phonon vibrations axe conceeded in the noise. As is known, Bi-2212 is of the pseudotetragonaJ structure (space group D^^) and the zero-center infraredactive vibrations are classified as six A2u modes along the c axis, and seven modes in the a6-plane.* Thus, we believe that these phonons are five of the ordinary in-pltine E« vibrations of the system. However, the phonon eigenfrequencies are not close to those previously reported by either experimental measurements or lattice dynamics calculation for pristine Bi2212.^^ It is likely that infrared phonon spectrum is perturbed to some extent by the structural changes associated with intercalation and could be quite different from that of a pristine crystal. Especially, the appearance of two phonons arovind 650 cm~\ where only one is expected in Bi-2212,*^^ suggests that the vibration contribution from the Bi-0 plane is strongly affected by iodine intercalation. Other features worth noting are the minimum or notch-like structures in the frequency range 400-500 cm~\ which result from the interaction between the c-axis LO phonon and the a6-plane bound carriers as has been discussed in det
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119 We now focus on the electronic contributions to the conductivity spectrum shown in Fig. 36. At low frequencies, the normal-state 10000 cm~^), the conductivity shows several electronic absorption bands as noted in the discussion of reflectance data. To compare the highfrequency conductivity of IBi-2212 with that of the pristine Bi-2212,^°^'^^^ we have plotted on a linear scale the (Ti(u;) spectra for both materials in the inset of Fig. 36. The first interband transition of Bi-2122, at ~ 19000 cm~\ usually assigned to the charge-transfer hand between 0 2p and Cu 3d in the Cu02 plane. In the case of IBi-2212, the intensity in this range is larger and the central energy occurs at lower frequencies (u ~ 17000 cm~^). The
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120 axe quite close to those seen in the (ti{u)) spectrum of IBi-2212. This suggests that the iodine is present as I J in IBi-2212. Less good agreement is obtained with the absorption at ~ 19230 cm"^ of the I2 molecule.^^^ Of course, it is possible both valence states of interceilated iodine atoms exist. Oscillator strength sum rule In order to give a quantitative basis of conductivity data, we have estimated the effective number of carriers (per planar Cu atom) participating in the optical transitions for energy less than hu). We show in Fig. 37 Ncff{u}), defined as^'' where m* is the effective mass of the carriers, m is the free-electron mass, V^ell is the imit cell volume, and A^cu is the number of CuO layers per unit cell. Here, we use Ncn = 2 for IBi-2212 an Bi-2212."' The effective mass is taken as the free-electron value. The results of evaluation of Eq. 19 in IBi-2212 for various temperatures are presented in Fig. 37. At each temperature, Nf.f[{u}) at first increases steeply at low frequencies due to the Drude-like band peaked at a; = 0, rises more slowly in the mid-infr
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121 show a reduction of spectrad weight in the whole frequency range as compared to the normal state curves. The area in (ti{u) from the superconducting state which appears in the S function at u; = 0 is not included in the ntmaerical integration which yields iVgif (w). The difference between Ncff{uj) above «ind below Tc therefore provides a good measure for the spectral weight in the superfluid condensate. We estimate the munber of effective Ccirriers per copper in the superfluid N3 = 7Veff(100 K) iVeff(10 K) = 0.108 ± 0.01. Turning to the comparison of the room-temperature Ncf[{u>) fimction for IBi2212 and Bi-2212,^°^'^'*^ shown in the inset of Fig. 37, we highlight two characteristic properties involved in the iodine intercalation. First, we obtain the values of iVtot to be 0.43 ± 0.03 for IBi-2212, and 0.38 ± 0.03 for Bi-2212. Second, for higher frequencies, the increased oscillator strength due to the electronic transitions associated with the iodine intercalation is readily evident. The larger iVtot ntmiber in IBi-2212 suggests that after iodine intercalation the total dopinginduced carriers in the Cu02 planes increase. The result is in accord with previous measurements of the Hall effect in IBi2212, which showed an increase of the hole concentration after intercalation. Here we emphasize that the difference of carrier concentration in IBi-2212 and pristine Bi-2212 is due to iodine intercalation, because the effects of small eimoimt of Pb doping in our Scimple can be negligible. Optical evidence of Pb doping (43%) in pristine Bi2212 shows the only 5% increase of hole concentration. As was stated above, the valence state of the intercalated iodine has been investigated by several groups. According to the optical results, neutral molecular iodine I2 alone seems unlikely because it cannot contribute to the increase of carrier density in the Cu02 planes. Instead, the iodine atoms must be ionized more or less to supply the Cu02 sheets with about 0.05 holes per Cu02 unit. The pressure dependence of the Hall coefficient also indicates that charge transfer occurs between intercalated io-

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122 dine atoms and Cu02 layers. Finally, it is necessary to point out that the increase in carrier density is favorable for the decrease in Tc from our experiments. We see no effect of interlayer coupling. However, the change c-aods resistivity in IBi-2212^^* implies that the interlayer coupling also plays a role. In addition, effect from the Bi-0 bilayer is still unknown. It is a delicate question to ask which mechanism, the doped hole concentration or the interlayer coupling or both, is responsible for the Tc reduction through intercedation. Quasiparticle scattering rate To understand better the effect of iodine intercalation on afr-plane optical conductivity, we analyzed the (Ti{ui) using "one-component" and "two-component" models. There has been much discussion over the one-component and the two-component pictures to describe the optical conductivity of high-Tg superconductors.* In the two-component model, there are two chcinnels of conductivity; (1) a Drude component with a temperature dependent quasiparticle scattering rate, and (2) a broad mid-infraxed component that is essentially temperature independent. In contrast, the arbitrary nature of the mid-infrared band in the two-component model has lead to the more general assimiption of the one-component, or generalized Drude model, in which the damping rate is frequency dependent. One — component model . We first made the generalized Drude analysis, in which the dielectric function is written as e^oj) Coo ^[rn*{uj)/m][u + i/T*{u)Y Here Coo is background dielectric associated with the chcirge-transfer and higher frequency contributions, m*(u;) and l/r*(u;) are the frequency-dependent (renormalized) mass and scattering rate of the charge carriers, and Up (the bare plasma frequency) = (20)

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123 ^-Knt^ I m* , with n the caxrier density. Another qucintity 1/t{(jj) = (m*/m)l/r*(u;) represents the unrenormalized qu«isiparticle scattering rate. For IBi-2212, we determined the values of e^o = 4.8 by fitting the 300K reflectance using a Drude-Lorentz model, and ix)p = 18300 cm~^ from integrating conductivity up to the charge-trcinsfer band in the simi-rule an«dysis (Eq. 19). Figure 38 shows the frequency dependent scattering rate 1/t{u)) of IBi-2212 for several temperatures. An astonishing linearity comes out for 800 cm~^ < < 4000 cm~^ at temperatures above and below Tg. The linear frequency dependence has been seen previously in the scattering rate of the cuprates at doping level ranging from lightly underdoped, optimally doped, to overdoped.^* On the other hand, the temperature variation in the high-frequency 1/t(u;) of IBi-2212 is similar to the behavior of some overdoped cuprates.^* However, in contrast to the linearity of 1/t{uj) spectrum, below 800 cm~^ the scattering rate falls faster than linearly and a threshold structure becomes more evident at lower temperatures. This behavior is like many underdoped cuprates where a distinct suppression of 1/t{uj) is observed below a characteristic energy (the pseudogap state) for T > TcJ^ At this point, somewhat puzzling is the pseudogap state persists even in the overdoped regime. For comparison, we used an expression for the dielectric function based on the marginal Fermi liquid theory (MFL)*^'^^ and the nested Fermi liquid theory (NFL).^^'^* The dielectric function in their theories can be written as ,2 = ^a,-2S(a,/2)l ' '''' where the factors of 2 arise because quasiparticle excitations come in pairs. The quantity S represents the quasiparticle self-energy of the charge carriers and the imaginary part of S (essentially the scattering rate) is given by Im E(u;) ~ < (22) 1 7rA<^u>, u > T

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124 Here A7 or A;^ a dimensionless coupling constant. For u < T the model predicts a renormalized scattering rate that is linear in temperature, as is expected from the linear temperature dependence in the resistivity that is observed in nearly aJl copperoxide superconductors. As u> increases, reaching a value of order of T or higher, a new spectrum of excitations arises. This causes the scattering rate to grow linearly with frequency up to a cutoff frequency u)c that is introduced in the model. The curves for — ImS(u;) of IBi-2212 are shown in Fig. 39. Clecirly, the linear behavior of the scattering rate exists only up to ~ 1500 cm~^ at each temperature. This low cutoff frequency has been previously pointed out by Romero et al.;^^^ the MFL approach is limited to a neirrow frequency range below 1000 cm~^ It seems necessary to allow for a second component in the optical conductivity at higher frequencies. According to the MFL prescription, we calculate the slope in the region where — ImS(a;) is w-linear at 300 K, to find a coupling constant A^^ ~ 0.34. We also notice that as the temperature is reduced the — Imll(a;) is depressed below 400 cm~\ which brings the uncertainty to estimate the linear slope of — Im S(a;) at low temperatures. Note that the energy scjile associated with the threshold structure in the — ImS(w) spectra obtained from the MFL analysis is two times smaller than the value in the l/r(c<;) spectra by using the generalized Drude approach, consistent with the fact that the MFL theory assimaes the qutisiparticle excitations coming in p«iir while it is purely single quasiparticle excitation in the generalized Drude model. Two — component picture . We now turn our attention to the two-component model. This is also referred to the DrudeLorentz model for the dielectric function: 2 N 2 <<^) = + E 2 y + ^00, (23) where and l/r/j are the plasma frequency and scattering rate of the Drude component, wy, Upj, and 7^ are the resonant frequency, oscillator strength, and the

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125 width of the j'^ Lorentz contribution. The method of tinalyzing the data is described in detail in earlier publications. We used N = 6 Lorentz oscillators in the fit, one 80-2000 cm~\ two of these bands fit the mid-infrared spectrum below 8000 cm~^ while three were required for the charge-transfer and higher bcinds. Above Tc, the fits indicate that the Drude contribution of IBi-2212 has a nearly temperature-independent plasma frequency, u)pD = 8900 ± 200 cm~\ which gives for the effective nimiber of free carriers per copper, Ndui^^ = 0.126 ± 0.01. We also foimd that the zero-frequency scattering rate I/tj) of the free-caixier or Drude contribution has a linear temperature dependence for T > Tc, whereas below Tc the scattering rate drops quickly, shown in Fig. 40. Writing h/tD = 2irXD ksT + h/TQ,^^^ with Xd the dimensionless coupling constant that couples the charge carriers to the temperatiure-dependent excitations responsible for the scattering, eind 1 /tq the zero temperature value assimaed to result from elastic scattering by impurities. We obtain Xj) ~ 0.25 and I/tq ~ 60 cm~^ Using the parameters of Drude plasma frequency ^pD ^ 8900 cm~^ aind the temperature dependence oH/td, the dc resistivity may be calculated as (pi, = (Wp£)T£)/60)~^ in imits f2-cm). This parameter is shown in the inset of Fig. 40, along with the transport data of a similar Scmiple.^®"* The far-infrared cind dc results are in fair agreement, in particular with regard to the linear behavior in resistivity with decreasing temperature. There is a discrepancy in the residual resistivity with a larger nonzero intercept for our sample in a linear extrapolation to r = 0. We estimate that the mean-free path for IBi-2212 (/ = vftd) is about 50 A at 100 K, taking the Fermi velocity of Bi-2212 to be = 2 x 10^ cm/sec^*^ and using our free-carrier relaxation rate of I/tq = 210 cm~^ This makes / > where the coherence length is typically about 10 ~ 15 A, which, together with the small value of Xd ~ 0.25, indeed suggests that IBi-2212 behaves like a clean-limit, weak-coupling system.

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126 Spectral weight in the condensate Prom the sum-rule analysis, we have obtained the effective number of the superconducting Ceirriers per copper for IBi-2212 as iV, = 0.108 ± 0.01. Expressed as the plasma frequency of the condensate UpS = y/Ainis^Irn where n, = iV, • iVcu/VJ^ is superfluid density, this translates to = 8300 ± 200 cm~^ The equivalent functions ei(a;), a^iu), [a2{u) = may also be used to give a estimate of the oscillator strength of the superconducting condensate. The real part of the dielectric function at several temperatures above and below Tc is shown below 1000 cm~^ in Fig. 41. The negative values of at low frequencies illustrate the metallic behavior of the system (characteristic of free carriers). As the temperature is lowered below Tc, t\(uj) shows a large negative value, indicating that inductive current dominates conduction current in the superconducting state. In a system where all of the normal-state Drude oscillator strength collapse into the superconducting S function at u; = 0, then this 8 fimction gives a contribution to e\{u) of ^iH = ^oo (24) Thus the uP' component of the very low-frequency ei(u;) measures the superfluid density. The inset of Fig. 41 shows ei(a;) vs at 10 K. The slope obtained from a linear regression fit gives Upg = 8000 ± 200 cm~\ which is only slightly smaller than the sum-rule value. Figure 42 shows the frequency-dependent penetration depth Ai(u;), defined as = v'c2/47ru; (Ti{u;) at low frequencies. The extrapolated zero-frequency value is about 1980 A, which is a Uttle larger than the 1860 A estimated for the pristine Bi-2212. The penetration depth is also related to the plasma frequency of

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127 the condensate, Ax, = cjups, so that a — > 0) = 1980 cnti"^ yields u^s = 8100 ± 200 cm~\ again in good agreement with the sum-rule value. Finally, we have used finite-frequency sum-rule analysis to obtain the effective number of carriers per planar Cu atom in (1) the low energy region below the chargertransfer band (iVtot = 0.43 ± 0.03), (2) the Drude or free carrier part from a twocomponent analysis (iVorude = 0.126 ± 0.01), and (3) the superconducting condensate {Ng — 0.108 ± 0.01). Considering the superconducting condensate fraction, it is found that the oscillator strength of the superfluid density contains about Ng/Ntot ~ 25% of the total doping-induced carriers or near Ns/Ndj^^c ~ 86% of the free-caxrier spectral weight in the normal state. These numbers are consistent with the basic clean-limit argument. Summary In summary, the a6-plane optical reflectance of IBi-2212 single crystal {Tc = 78 K) has been measured over a wide frequency range above and below Tc. A clear observation of differences on the infrared vibrationeJ spectrum and the visible-tdtraviolet interband transitions, compared to the pristine crystal, indicates that the intercalation of iodine does affect the in-plane optical response. Based on the conductivity data, we find that upon intercalation the low-frequency spectral weight increases; that is the increase of hole concentration in the Cu02 planes. This behavior can be understood as due to holes introduced by intercalated iodine in the Cu02 planes. The iodine is present cis ions, most likely as Ij. We see no effect of interlayer coupling. However, the cheinge c-axis resistivity in IBi-2212^^^ implies that the interlayer coupling also plays a role. We have also employed both the one-component and the two-component models of the a6-plane optical conductivity in order to investigate the effects of iodine intercalation on the quasiparticle scattering rate. Within the framework of the general-

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128 ized Drude model and maxginaJ Fermi liquid theory, the appecirance of low-frequency suppression in the scattering rate is similar to the behavior of many underdoped cupratesJ^ In contrast, the temperature vciriation of the high-frequency part of the scattering rate is close to what occurs in some overdoped cuprates J® Alternatively, the zero-frequency scattering rate Ifrj) from the free-carrier contributions varies linearly with temperature for T > Tc and decreases quickly below Tc. 1/td from the inelastic scattering process puts our Scimple in the weak-coupling regime {Xd ^ 0.25), In the superconducting state, a superconducting condensate is evident in the lowfrequency a6-plane optical data; there is a considerable transfer of oscillator strength from the far-infrared region to the S function response of the superconductor. A simirule evaluation finds the superfluid density contains about 25% of the total dopinginduced, or necirly 86% of the free-carrier oscillator strength in the normal state. These numbers are consistent with the basic clean-limit argimient. The value of the superconducting penetration depth has been estimated to be 1980 A, slightly larger than the 1860 A found in pristine Bi2Sr2CaCu208.

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129 Photon Energy (eV) 0.01 0.1 1 .0 I -I ~ !_ -! L ' — ' ' ' I ' ' ' ' — ' — ' 100 1000 10000 Frequency (cm~^) Fig. 35 The aft-plane optical reflectance of iodine-intercalated Bii.9Pbo.iSr2CaCu208+« in the entire frequency range at different temperatures above and below Tc. For comparison, inset shows the 300-K reflectance spectra of IBi-2212 and Bi-2212.i°^'i''i

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130 0.01 5000 Photon Energy (eV) 0.1 1 -T 1 1 1 — I — rIBI-2212 4000 3000 2000 1000 300 K 5000 200 K 4000 100 K 45 K o T 3000 10 K a 2000 3 ' — ' 1000 0 _ T = 300 K 1 — I — I — r -1 — I — I — I — I — 1 — r IBI-2212 BI-2212 -I 30000 100 1000 10000 Frequency (cm~^) Fig. 36 The real part of the optical conductivity for iodine-intercalated Bii.9Pbo.iSr2CaCu208+6, calculated through KramersKronig analysis of the reflectance spectra presented in Fig. 35. The arrows denote vibrations which are present in the 10-K spectrum. The inset displays the room temperature
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131 Photon Energy (eV) 0 12 3 Frequency (cm ) Fig. 37 The effective number of carriers per planar Cu atom as a fimction of frequency and temperature for iodine-intercalated Bii.9Pbo.iSr2CaCu208+i, obtained from an integration of the conductivity using Eq. 19. The inset shows the effective carrier numbers for IBi-2212 and Bi-2212.^°^'i'*i

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132 Photon Energy (meV) 0 100 200 300 400 IBi-2212 300 K Fig. 38 The temperature-dependent quasiparticle scattering rate 1/T(a;) obtained from the generaHzed Drude model (Eq. 20) for iodine-intercalated Bii.gPbo.i Sr2CaCu2 Os+s

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133 Photon Energy (meV) Fig. 39 The imaginary part of the self-energy Im E(a;) for iodine-intercalated Bii.9Pbo.iSr2CaCu208+i obtained from the marginal Fermi liquid theory (Eq. 21) at several temperatures.

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134 Fig. 40 The zero-frequency scattering rate 1/t/j (symbols) of the free-carrier contribution from the two-component fit (Eq. 23) to the optical conductivity of iodine-intercalated Bii.9Pbo.iSr2CaCu208+«. The straight line shows a linear fit to the temperature dependence of 1/t£) above Tc. The inset shows the dc resistivity (symbols) from the infrared measurements and the transport data (dashed line) of a similar sample, obtained by Xiang et al}^*

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135 Photon Energy (meV) 0 20 40 60 80 100 120 0 200 400 600 800 1000 Frequency (cm~^) Fig. 41 The real part of the dielectric function ei(a;) (from KramersKronig transformation) at several temperatures for iodine-intercalated Bii.9Pbo.iSr2CaCu208+«. Inset: a plot of €i{u;) (dashed line) vs uj-^ at 10 K. The range of the data shown is 500-100 cm"^. The linear fit is shown by the solid line.

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136 3000 2500 o< 2000 1500 1000 Photon Energy (meV) 20 40 60 80 0 100 200 300 400 500 600 700 800 Frequency (cm~^) Fig. 42 The frequency-dependent superconducting penetration depth Ai(u;) of iodine-intercalated Bii.gPbo.iSrzCaCuzOs+i at 10 K. The values of Ai(0) from the sum-rule analysis are indicated by the symbol.

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CHAPTER VI AB-PLANE OPTICAL PROPERTIES OF NI-DOPED Bi2Sr2CaCu08+i Introduction The eflFect of impurity substitutional doping on high-Tg superconductors has received a great deal of attention in recent yeaxs.^^"^ Particxilar interest arises about the influence of 3d transition-metaJ ions substituted for the in-plane copper atoms Cu(2) because it is generally believed that the most important element of the superconducting cuprates is the two-dimensional Cu02 plane. Among the many possibilities, Ni and Zn are the only dopants for which there is substantial evidence for substitution in the Cu02 planes. The most prominent change of electronic properties brought on by Ni and Zn substitution is the strong suppression of Tc, with Zn suppressing Tc at a rate (10 K/at.%) about twice that of Ni.^^^ A further issue is the effect on Tc reduction of magnetic (Ni) vs noimiagnetic (Zn) dopants.^®^ Magnetic impurities are known to suppress Tc due to Abrikosov-Gor'kov pair breaking,^*' whereas Anderson's theorem^®^ states that nonmagnetic impurities do not affect Tc. The effect of dopants on the superconducting properties of high-Tc materials is considerably different from conventional superconductors.^*^ So far, a large ntmibers of experimental studies of Ni and Zn doping have concentrated on YBa2Cu307_i (Y123) systems. However, substitutional effects in Y123 can easily be confused by accompanying changes in oxygen content. In contrast, Bi2Sr2CaCu208+i (Bi-2212) offers a simpler possibility to probe the intrinsic response of the Cu02 planes in the presence of transition-metal dopants because there are no 137

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138 chains in these Bi-based compounds, edthough there is a superlattice structure along the b axis. In this chapter, we discussed the a6-plane reflectance of a Bi2Sr2Ca(Cui_iNix)208+i (z = 0.0215) single crystal over the frequency range from far-infraied to the near ultraviolet in both normal and superconducting states. To the best of our knowledge, there have been no reports on the far-infraxed optical properties of Ni-doped Bi-2212 samples. We will compare our Ni-doped data with results for undoped Bi-2212 samplgg35,i07,i4l 3^ g^Qjj. Yeain how Ni substitution affects the afr-plane optical properties at temperatures above and below Tc. Experimental Techniques and Data AncJvsis Our single crystal of Bi2Sr2Ca(Cui_^Nix)208+6 (x = 0.0215) was grown using the conventional self-flux method. The Ni content was determined by electron-probe microanalysis (EPMA). The crystal had a dimension about 4 x 4 x 0.1 mm^. The sample shows an onset of Tc in ac susceptibility at 70 K, with transition width ATc = 5 K. Characterizations of dc resistivity and angle-resolved ultraviolet photoemission spectroscopy (ARUPS) have also bee performed on similar samples. The resistivity data shows a linear temperature variation and a large residual resistivity. The at-plane optical reflectance has been measured from 80-40000 cm~^ (10 meV-5 eV). We used a Bruker IPS 113v Fourier transform spectrometer to cover the frequency range from 80 cm"^ to 4000 cm"^ and a flow cryostat for the temperature variation from 300 K down to 20 K. Room-temperature reflectance spectra were coUected from 1000 cm"! up to 40000 cm"^ by using a Perkin-Elmer 16U grating spectrometer. Under a microscope, the sample had optically flat and shiny surface, so no attempt was made to coat the surface with aluminum to correct for scattering loss.

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139 The optical conductivity was derived by the Kramers-Kronig analysis of the reflectance spectrum. To perform this transformation one needs to extrapolate the reflectance at both low cind high frequencies. In the normal state, we modeled the reflectance using the Drude-Lorentz model, while below Tc the two-fluid model was used. Then, we used the fitted results to extend the reflecteince from the lowest frequency measured in the experiment to a; w 0. The Hagen-Rubens relation yras also used as an extrapolation to low frequencies above Tc. Above 100 cm~^ the optical conductivity is not sensitive to the choice of low-frequency approximation. For high frequency extrapolation, the temperature dependent data up to 4000 cm~^ yras joined smoothly with the measured high frequency room temperature result. Between the 40000 and 320000 cm~\ the reflectance was merged with the pure Bi-2212 results of Terasaki et al}^^; beyond this frequency range a free-electronlike behavior of uj~* was assimied. We will evciluate on optical conductivity using a partial sum rule, estimating the spectral weight in terms of the effective number of carriers per Cu02 pl«ine;*° 0 where m* is the effective mass of the carriers, m is the free-electron mass, VJ«u is the unit cell volimae, and Ncn is the nimiiber of CuO layers per imit cell. Here, we use iVcu = 2 for the Bi-2212 materials. The effective mass is taken as the free-electron value. Nef[{u) is proportional to the number of carriers participating in the optical excitations up to Hlj.

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140 Comparison of Ni-Doped to Pure Bi9!Sr9CaCu9Q« The upper panel of Fig. 43 compares the reflectance at 300 K to pure Bi-2212 sample over the entire measured frequency range. The most striking difference is that the reflectance of Ni-doped crystal is significantly lower below 3000 cm~^ thzin in the pure material, indicating that Ni impurities modify the electronic structure ne«ir the Fermi level. In contrast, the reflectance above 3000 cm~^ up to a plasma miniTniim aroimd 10000 cm~^ is not eiffected by Ni substitution. At higher frequencies, two interband transitions «ire evident. The strength of the 16000 cm~* (2 eV) peak for the Ni-doped sample is weaker than that for the imdoped case, while the intensity of 30000 cm~^ (3.8 eV) band is similar for both samples. All of the above observations for the Ni-doped crystcd are quite different from those in the carrier-depleted case, where the rearrangement of spectral weight occurs from 0 eV up to several eV. A comparison of the roomtemperature optical conductivity for the pure and Nidoped Bi-2212 crystals is presented up to 40000 cm-1 in the middle panel of Fig. 43. In pure system, the low-frequency conductivity is dominated by free-ceirrier behavior (a Drude absorption at w = 0). Ni modifies significantly the
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141 compaxing the CT peak of insulators La2Cu04 with that of La2Ni04. In La2Cu04, the CT excitation is seen at about 2 eV, while in La2Ni04 the CT gap moves towards 4-5 eV.'*^ With regards to the second electronic peak near 30000 cm~\ both samples roughly resemble each other. The excitation is possibly eissociated with transitions occurring in the Bi-0 layers and not in the Cu02 planes. Still, the identification of this band remains controversial. ^^^"^^^ In the lower panel of Fig. 43 we plot the room-temperature results of the pure and Ni-doped crystals. In both materials, A^eff(w) at first increases rapidly in the infreired region, begins to level off near 8000 cm~\ cind then rises again above the onset of the charge-transfer band. However, the overall magnitude for the Ni-doped crystal is slightly smaller than of the pure sample in the studied spectral range. In order to give a quantitative value of the effective number of carriers, we take as the niunber of at ~ 14500 cm~\ just before the influence of the charge-transfer band begins to dominate the results. Then, the spectral weight below the onset of the chargetransfer gap corresponds to an effective number of total carriers per copper, iVtot, of ~ 0.38 and 0.34 for the pure and Ni-doped samples respectively. Our results provide evidence that Ni likely substitutes as Ni2+ for Cu^"*"". The 0.03-0.04 reduction in iVtot for our Ni-doped sample with a Ni content of cni = 4.3 at.% suggests that each Ni removes one Ccirrier. Temperature Dependence of Ni-Doped Reflectance spectrum The afr-plane reflectance of the Ni-doped crystal is shown between 80 and 2000 cm-' at temperatures above and below Tc in Fig. 44. The absolute value of the room-temperature reflectance is over 70% for w < 2000 cm-^ When the sample is cooled, there is a substantial temperature dependence in the reflectance over the entire

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142 spectral range. The reflectance increases rapidly with decreasing temperature. Below 75 K, it is also interesting that above 600 cm~^ there is no temperature dependence. In the superconducting state, the reflectance is not close to unity down to the low frequency limit of our measurements. Such behavior is different from that of imdoped Bi-2212, for which the reflectance is quite high, cind is greater than. 99% below ~ 200 cm"^ at T < Tc.^"'^'^*^ This difference clearly suggests that Ni impurities disturb the superconductivity. Another feature worth noting is the shoulder-like structure developing in the reflectance at w ~ 500 cm~\ a common behavior in many of the cuprate superconductors.^' Conductivity and dielectric function The real part of optical conductivity (Ti{uj) is shown below 2000 cm~^ and for several temperatures in Fig. 45. There is unusual behavior of optical conductivity below 2000 cm . The 300K spectrimi consists of a broad maximum approximately 400 cm~\ which grows in intensity and shifts to lower frequency as the temperature is lowered. Below Tc, we observe a decrease of low-frequency spectral weight associated with the formation of the superconducting condensate. However, a strong peak near 100 cm~^ is still visible down to 20 K. This peculiar feature is present through the whole measured temperature range. The inset of Fig. 45 compares the 20-K data for Ni-doped to undoped Bi-2212.^°^'^'*^ There is clearly a much larger conductivity with former case. Here we must emphasize that the conductivity maximum peak itself is not a experimental artifact. We checked the low-frequency extrapolation does not affect the result qualitatively. Furthermore, the dc conductivity values at 300 and 100 K, reported by Quitmann et al.^^^ for crystals similar to ours, are marked along the vertical axis of Fig. 45. They are much lower than the value of the frequency dependent conductivity maximum, but there is a fair agreement between the far-infrared ai{u} -> 0) and the dc conductivities. A similar broad low frequency peak has been

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143 observed for other highTc superconducting materiaJs, which aie either intrinsically or deliberately disordered including Bi2Sr2Cu06 (Bi-2201),^" Pb2Sr2(Y/Ca)Cu308,^^* and Tl2Ba2Cu06+« (T12201).^*^ The conductivity peak Wcis also seen in the response of Y123 single crystal eifter low energy He"*" ion irradiation^'^ and Zn-doped or Nidoped Y123 fibos^^" as well as a-axis Zn-doped YBa2Cu408 (Y124).i^^ Considering all of the above, we believe that the observed finite frequency pealc is an intrinsic response of the disorderd Cu02 plane. The KramersKronig-derived real part of the frequency-dependent dielectric function, ei(a;), is shown in Fig. 46. At high frequencies, ei(u;) is negative at all temperatures and the zero crossing corresponds the location of the screened plasma frequency. Below 500 cm~^ the dielectric function rises dramatically to positive values for the normal-state curves, but drops sharply upon entry into the superconducting state. We attribute the positive low-frequency ei(u;) at high temperatures to the gradual development of the strong peak in far-infrared
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144 where Cqo is a constant term, and Upj) and 1/td are the pljisma frequency cind scattering rate of the Drude (free caxrier) component, and Upj, wy, ajid 7) are the oscillator strength, the resonant frequency, and the width of the j*^ Lorenti (bound carrier excitation) contribution. The real part of the optical conductivity is calculated from the imaginary part of the dielectric function (Ti{u>) = a;c2(w)/47r. The details of the fit aie rather complicated because of the many parameters. We have tried to fit the room-temperature conductivity spectrum in the whole frequency range with a Drude part, four Lorentzian oscillators below 8000 cm~^ (not counting phonon), eind three above the chargetrajisfer gap. We used the preliminary parameters and made a least-squares fit to the experimentally measured reflectance. Because the temperature-dependent data extend only to 4000 cm~*, we fixed the parameters for the higher frequency oscillators with u > 6000 cm~^. In addition, we fixed Cqo = 3.0. Then we varied the Drude parameter and three mid-infrMed oscillators to fit the measured reflectance below 4000 cm~^ at 200, 150, 100, and 75 K. The parameters are listed in Table 6. The results for the fit are compared to the low-energy portion (u < 2000 cm~^) of the conductivity in Fig. 47. In our fits, two absorption peciks appear in the mid-infrared region. One is around 1000 cm , with its position shifting to a slightly lower frequency and its magnitude decreasing as the temperature is reduced. The other, at about 1875 cm~^ has little a small systematic temperature variation. In contrast, the lowest frequency Lorentz mode, which is near 400 cm~^ at 300 K, acquires a progressively more spectral weight while its center frequency of the peak decreases from 420 cm~^ to 106 cm~^ One point that may be relevant for this mode is the likely presence of significant disorder induced by Ni impurities. The behavior may thus reflect the localization of carriers in the Cu02 planes induced by Ni substitution. Indeed, a peak in the conductivity centered at finite frequency is a generic feature of disordered conductors and has

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145 Table 6. Paxameters of a two-component oscillator fit to the meaisiired reflectance below 4000 cm-^ at 300, 200, 150, 100, and 75 K. All units are in cm~^. r = 300 K r = 200 K r = 150 K T = 100 K r = 75 K 8280 8666 8687 8530 8657 ^/td 1151 871 710 568 504 4124 5643 6842 7400 7768 Wl 402 288 225 149 106 71 821 559 413 276 182 9877 8926 7891 6906 5719 1017 1014 966 955 950 72 2623 2234 1839 1815 1774 8219 7749 8243 9391 10420 ij^i 1875 1866 1883 1857 1883 73 7746 10711 12516 10529 623 been observed in disordered doped semiconductors^^^"^^^ as well as conducting polymers. Note that the Drude-like response persists with constant spectral weight while the peak at finite frequency produces the additional feature on the top of the Drude background. The Drude plasma frequency, Wp/j = 8500 ± 200 cm'^ is essentially temperature-independent. The spectral weight of the additional peak grows with decreasing temperature, but never exceeds that of the Drude contributions. In Fig. 48 we compare the temperatiire-dependent scattering rate I/t^j for pure and Ni-doped crystals. It is clear from the plot that l/r/) for both samples has a Hnear temperature dependence above Tc. However, the Ni-doped material has a larger scattering rate. Writing hlro = 2i^\d kgT + H/to,^^^ where Xd is the dimensionless coupling constant that couples the charge carriers to the temperature-

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146 dependent excitations responsible for the scattering and the temperature-independent term I/tq is assumed to result from elastic scattering by impurities. We obtain ~ 0.28 and 1/ro ~ 10 cm"^ for pure Bi-2212 sample, Ai) ~ 0.46 and I/tq ~ 282 cm~^ for the Ni-doped sample. This result indicates that the effect of Ni on the conduction carriers is both to increase their elastic scattering rate and the coupling between the carriers and the excitation or the excitation itself. Using the Drude plasma frequency ijJpD ~ 8500 cm~^ and the temperature dependence of 1/t/j, the do resistivity may be calculated [/?,> = (Wp£,T/)/60)~^, in imit fi-cm]. This quzmtity is shown in the inset of Fig. 48, compared to transport meeisurements of a similar sample.^®* The dc resistivity deduced from the optical measurements is in fair agreement with the transport results, in particular with regard to the linear behavior in resistivity with decreasing temperature. However, the dc and far-infrared resistivity differ by about a factor of 2; at 300 K ~ 2 mO whereas />,> ~ 1 ml). Additionally, there exists difference in the residual resistivity with a smaller nonzero intercept for our szimple in a linear extrapolation to T = 0. The most possible origin for these discrepancies, as pointed out by Ref. 8, is that due to the irregtilar shape of the crystals after cleavage the absolute values of the dc resistivity cire only approximate. Below Tc, the quasiparticle scattering rate decreases qmckly in pure Bi-2212, falling from the large values caused by inelastic scattering rate above Tc to a low value that controlled by impmrity scattering in the superconducting state. However, the addition of Ni so limits the decrease in 1/r/) that there is no indication of a drop in the scattering rate near Tc. Previous infrared measurements on Ni-doped Y123 films^^" have also found the fitted scattering rate decreases smoothly as T is lowered; no evidence for an abrupt change occurs near Tc. It is worth pointing out that the low temperature value of 1/t/j(20 K) approaches to zero in the pure sample. On the contrary, in the Ni-doped system, the l/r£> is very close to the extrapolated intercept

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147 1 /to of the linear regime above Tc. This behavior must be tciken into account in the later discussion of any property in the superconducting state that is sensitive to the impurity eflPects. One-component analvsis It is instructive to explore the effects of Ni impurities on the frequency-dependent scattering rate within the so-called one component analysis of a\{uj). We first consider the generalized Drude analysis, in which the dielectric function is written as ' ' °° u;[Tn*{uj)/m][u + i/r*{u)y ^ ^ Here m*(w) and 1/t*{u) are the frequency-dependent (renormalized) mass and scattering rate of the charge carriers, and ujp (the bare plasma frequency) = -yiTrne^/m*, with n the carrier density. Another quantity 1/t{u>) = (m*/m)l/r*(a;) represents the unrenormalized quasiparticle scattering rate. In the Ni-doped sample, the haie plasma frequency ujp = 15650 cm"' can be determined from integrating optical conductivity up to the charge-transfer band in the simi-rule analysis. Figure 49 shows the frequency-dependent scattering rate 1/t{uj) at several temperatures. Ni doping causes drastic changes in the room-temperature l/r(a;) as compared to the piure Bi-2212 sample, also shown in the inset of Fig. 49. For x = 0.0, the increases with frequency in a linear fashion, as has been pointed out many times previously. With Ni substitution, the scattering rate is enhanced over the entire spectral range. The frequency dependence is quite modest, and a 1/a; behavior occurs at low frequency. The larger 1/t{u) for the Ni-doped crystal suggests an increase in elastic scattering. The 1/u; behavior in the low-frequency 1/t{u) spectrum can be considered as related to localization of carriers in the Cu02 planes initiated by Ni impurities. A similar behavior is also observed in disorderd T1220l'*^ and

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148 Zn-doped Y124.^^^ When the temperature is decreased from 300 K to 75 K, 1/t{u) shifts significantly downward; changes with temperature below 75 K aie much less prominent. The behavior of l/r(a;) differs from those of imderdoped cuprates in two ways J* First, in underdoped materials the high-frequency part of 1/t{u}) is effectively temperature-independent. Second, there is no indication of any suppression of 1/t{uj) below a characteristic energy (the pseudogap state) for T > Tc. A very similar approach was an expression for the dielectric function based on the marginal Fermi liquid (MFL) theory*^ -^^ and the nested Fermi liquid (NFL) theory.^^'^* The dielectric function can be written as e(w) = Coo —r ^f,, (28) where the factors of 2 arise because quasiparticle excitations come in pjiirs. The qucintity S is the quasiparticle self-energy of the charge carriers; and the imaginary part of E (essentially the scattering rate) is given by -ImS(u;)~.^ . (29) Here or A^, is a dimensionless coupling constant. For u; < T the model predicts a renormalized scattering rate that is linear in temperature, which is expected from the linear temperature dependence in the resistivity that is observed in nearly all copper-oxide superconductors. As a; increases, reaching a magnitude of order of T or higher, quasiparticle interactions cause the scattering rate to grow linearly with frequency up to a cutoff frequency Wc that is introduced in the model. -ImS(a;) for the Ni-doped crystal is shown in Fig. 50. Clearly, Ni impurities induce a novel feature in the ImS(u;) spectra which is a region of the negative slope below ~ 250 cm'^ This behavior of the scattering rate suggests that substitution

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149 with Ni strongly suppresses carrier mobility at low frequencies. A negative slope has been theoretically predicted for disordered two-dimensional conductor. Above 250 cm , the linear behavior of the scattering rate exists only up to ~ 1200 cm ^ at each temperature. This low cutoff frequency has been previously pointed out by Romero et a/.^^^ to imply that the MFL approach is limited to a narrow frequency range. It seems necessary to allow for a second component in the optical conductivity at higher frequencies. According to the MFL prescription, we calculate the slope of -Imi;(a;) between 250 cm~^ and 1200 cm"^ at 300 K, which yields a coupling constant A^^ ~ 0.06. While at 75 K this number is a factor of 2.5 larger, A,^ ~ 0.15. These results are much smaller than the coupling constant obtained from the Drude contribution only, A/j ~ 0.46 (and much smaller than the 0.30 typically found in pure crystals^). This discrepancy suggests that one-component model of charge transport for the Ni-doped system where, cri (u) shows a finite frequency peak in the far-infrared region rather than a smooth free-carrier band with excess conductivity at high frequencies, may be inappropriate. Spectral weight We now turn our attention to the temperature-dependent behavior of spectral weight, shown in Fig. 51. The curves were obtained by using Eq. 25. There is some variation in normal-state iVeff(a;) with temperature. As the temperature is reduced, the spectral weight first shifts to lower, but nonzero frequency; this is reflected in the progressive increase in the intensity of of low-frequency conductivity with decreasing temperature, shown in Fig. 45. In the superconducting state, N^{u) is smaller overall. The missing area in = 0, which is not included in the numerical integration of Eq. 25. The difference in iVeff(a;) in the normal and superconducting states above and below Tc provides a good measure for the spectral weight in the superconducting condensate.

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150 We estimate the number of effective carriers per copper in the superfluid Ns = iVgff (75 K) iVeff(20 K) = 0.062 ± 0.01. The value of the Drude plasma frequency from the two-component analysis is converted into the effective nimiber of the free-carrier part, ^Drude = 0-092 ± 0.01 per copper. The effective number of the total carriers is iVtot = 0.34 ± 0.03. It turns out from the sum-rule analysis described above that the a fraction of Ns/Ntot and iVa/A^Drude is found to be 20% and 67%. Thus only about a fifth of the total doping-induced spectral weight appears in the S function at a; = 0; the remainder is at finite frequencies. If the two-component picture is adopted, then 67% of the free-carrier spectral weight condenses, behavior that we discuss below. Superconducting-state properties The inset of Fig. 45 compares the 20-K conductivity of pure eind Ni-doped crystals. The 20-K
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151 doped cuprates. The data points for the pure Y123 and Bi-2212 crystals lie on what is generally referred to as the Uemura line. This linear relationship between Tc and Us has been observed in mciny underdoped and optimally-doped cuprates. The data for the Ni-doped crystcd axe horizontally offset from the imiversal plot, with a smaller superfluid density than implied by Tc. The decreased superfluid density is most likely associated with impurity-induced disorder. Except for lightly Ni-doped (1.4 %) Y123 single crystal,^" which lies neax the Uemura line, our results axe like but smaller than previous observations of very large reductions in superfluid density for Ni-doped (2%, 4%, and 6%) Y123 films.^^O-^^^'^^^ In films, infrared measurements find no difference at all in
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152 Ai = clups, a Ai(a; 0) = 2270 cm"^ yields = 7010 ± 200 cm-^ All of the above methods give consistent results for the spectral weight of the 8 function. Summarv In summeiry, we report the a6-plane optical reflectance of single crystal of Bi2Sr2Ca(Cui_xNix)2084.j, for x = 0.0215, over a wide frequency range above and below Tc. It is found that Ni doping affects not only the normal state, but also the superconductivity. In the normal state, Ni substitution causes a drastic change in the frequencydependent optical conductivity. Instead of cri{u}) monotonically decreasing with frequency at low frequencies (i.e., Drude behavior), a broad peak appears, centered at ~ 400 cm~^, which grows in intensity and shifts to lower frequency as the temperature is reduced. A Drude-like contribution remains as well. The superconducting state conductivity is also anomalous. There is no sign of an energy gap, but a finite frequency peak in the normal state is still visible down to 20 K. It is importcint to realize that the observed bump in (Ti(u;) Ccinnot be explciined by the low-frequency extrapolation. We suggest that this peculiar low-frequency feature is associated with the significant disorder induced by Ni impurities. Based on the conductivity data, we have investigated the behavior of the quasipeirticle scattering rate through Ni substitution within both two-component and onecomponent pictures. The normal-state 1 /r/j of the Drude contribution shows that the primary effect of Ni on the conduction carriers is to increase their elastic scattering rate. There is no indication of a rapid drop in 1/td just below Tc as compared to the pure Bi-2212. Alternatively, the frequency-dependent scattering rate obt«iined from the generalized Drude model and marginal Fermi liquid theory suggests that Ni also acts as an impurity and the effect is additive. A l/cj behavior in the low-frequency scattering rate spectra can be considered as localization of carriers in the Cu02 planes initiated by Ni impurities.

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153 Estimate of the low-frequency spectral weight shows that Ni reduces the carrier density in the Cu02 plane: each Ni removes one carrier. Below Tc, we observe a decrease of low-frequency spectral weight in the conductivity spectra, although there is a lot of low-energy oscillator strength remaining. The superconducting penetration depth, calciilated from this missing area, is about 2270 A. A sum-rule evaluation finds the superfluid contains about a fifth of the total doping-induced, or two thirds of the free-carrier oscillator strength in the normal state. The strength of the condensate is horizontally offset from the Uemura line, with a smaller superfluid density than implied by Tc. This decreased superfluid density in the Cu02 plane could be connected with the effect of impurity-induced disorder. We can compare the optical data with other experimental restilts, including ARUPS and microwave measurements. Room-temperatvire ARUPS spectra^®^ for a crystal similar to ours show that Ni doping affects the electronic band structure. The disappearance of the dispersing bandlike state suggests a modification of the Fermi surface. There is a evidence for the spectrcil weight shifting from the dispersing bandlike state into an incoherent background of states elastically scattered by Ni impurities. In agreement with our results, Ni acts primarily to induce disorder tind leads to a radical alteration of the Drude feature into finite frequency peak in the conductivity spectra. There is a connection between the impurity studies presented here and the microwave results. ^''^ We note a resemblance of the scattering rate l/r/j from the free-caxrier contributions to the microwave data obtained with the Ni-doped Y123 single crystals. Siurface impedance results indicate that Ni impurities provide strong elastic scattering that limits the collapse of the scattering rate near Tc and suppresses the peaic in the surface resistance. Furthermore, comparison of the effect of Ni and Zn impurities on the temperature dependence of the London penetration depth suggests that Ni does not have such a strong pair-breaking effect as Zn impu-

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154 rity, which is cJso consistent with our observations on the behavior of the superfluid density.

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155 0.01 1 .0 Photon Energy (eV) 0.1 1 CD O c o "o 0.5 0.0 E o 2000 ~i 1 1 — r — 1 — r— r~i — 1 — I — r— r0.5 0.0 T = 300 K X = 0.0215 X = 0.0 H 1 — I I I I I H 1 — I I I I I H [X = 0.0215 X = 0.0 Frequency (cm ^) Fig. 43 The 300-K reflectance (upper), real part of conductivity (middle), and the effective carrier numbers (lower) spectra of the pvire (dashed line) and Ni-doped (solid line) Bi2Sr2CaCu208+6 crystals in the entire frequency range.i»7'"i

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156 O c o o _a) M— 0) 50 Photon Energy (meV) 100 150 200 T 1 1 r 1.0 0.9 0.8 0.7 20 K 50 K 75 K 100 K 150 K 200 K 300 K T 1 1 r Bi2Sr2Ca(Cui_,Nij208-,5 X = 0.0215 0.6 _L -I 1 I L. 500 1000 1500 Frequency (cm~^) -1 I L. 2000 Fig. 44 The a6-plane optical reflectance of Ni-doped Bi2Sr2CaCu208+« from 80 to 2000 cm~^ and at temperatures above and below Z..

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157 50 Photon Energy (meV) 100 150 200 E o 3 b 10000 8000 6000 4000 2000 -I 1 r Bi2Sr2Ca(Cui_,Nij20a+5 T T 1 r = 0.0215 I I I I I I I r I I I I I I I I I I T = 20 K X = 0,0215 X = 0.0 _ J. 500 1000 1500 Frequency (cm~^) 2000 Fig. 45 The real part of the optical conductivity for Ni-doped Bi2Sr2CaCu208+5, calculated by KramersKronig analysis of the reflectance spectra. The symbols on the vertical axis show the dc conductivities at 75 and 300 K for crystals similar to ours.^^^ The inset displays the 20-K (Ti{u) spectra of the pure (dashed line) and Ni-doped (solid line) Bi-2212 crystals.^°^>i'*i

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158 5 I 1 1 1 1 1 I 1 I I I 0 200 400 600 800 1000 Frequency (cm~^) Fig. 46 The real part of the dielectric function ei(u;) (from KramersKronig transformation) at several temperatures for Ni-doped Bi2Sr2CaCu208+«.

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159 Fig. 47 The optical conductivity (solid line) of Ni-doped Bi2Sr2CaCu208+« at 300, 200, 150, 100, and 75 K compared to conductivity (long dashed line) from the two-component oscillator fit. The various terms in the fits are also shown: the Drude band (dash-dotted Une) and three Lorentz oscillators (short dashed line).

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160 2000 I — I — I — I — I — I — I — I — I — I — I — ' — ' — ' — ' — I — ' ' ' ' I ^ 0 50 100 150 200 250 300 Temperature (K) Fig. 48 The free-caxrier scattering rate l/r/j (symbols) of the pure (filled circles) and Ni-doped (filled triangles) Bi-2212 crystals from the twocomponent fit (Eq. 26). The straight line shows a linear fit to the temperature dependence of 1/td above Tc. The inset shows the infrared resistivity (filled triangles) from the optical measurements of Ni-doped Bi2Sr2CaCu208+tf and the dc resistivity from transport measurements (dashed Hne) of a similcir Scimple.^*^

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161 Photon Energy (meV) 50 100 150 200 6000 5000 7 4000 E o 3000 T 1 1 r -1 1 1 r Bi2Sr2Ca(Cui_^Nij2084-c5 X = 0.0215 6000 _ \ 300 K 200 K 150 K 100 K 75 K 50 K 20 K \ 2000 1000 ^ E 4000 V 2000 —I — I — I — I — I — 1 — 1 — I — I — 1 — I — I — I — I — I — I — ' T T = 300 K X = 0.0215 X = 0.0 I I I ^ ^ I 1 I I I I I ! I I 1 500 1000 1500 2000« (cm"') 500 1000 1500 2000 Frequency (cm ^) Fig. 49 The temperature-dependent quasipaxticle scattering rate 1/t{w) obtained from the generalized Drude model (Eq. 27) for Ni-doped Bi2Sr2CaCu208+*. The inset displays the roomtemperature 1/t{uj) spectra of the pure (dashed line) and Ni-doped (solid line) Bi-2212 crystals.

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162 Photon Energy (meV) 50 100 150 200 3000 2000 1000 500 1000 1500 Frequency (cm~^) 2000 Fig. 50 The imaginary part of the self-energy -ImS(a;) for Ni-doped Bi2Sr2CaCu208+5 obtained from the marginal Fermi liquid theory (Eq. 28) at several temperatures.

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163 50 Photon Energy (meV) 100 150 200 -I 1 1 r -1 1 1 r -I 1 1 r T Bi2Sr2Ca(Cui_,NIj208-f<5 X = 0.0215 300 K 200 K 150 K 100 K 75 K 50 K 20 K 500 1000 1500 Frequency (cm~^) 2000 Fig. 51 The effective number of carriers per planar Cu atom as a function of frequency and temperature for Ni-doped Bi2Sr2CaCu208+« obtained from an integration of the conductivity using Eq. 25.

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164 o 160 140 120 100 80 60 40 20 h 0< 3000 2000 1000 + T Bl2Sr2Ca(Cu,_J^tj2084^ X 0.0215 20 K I 200 400 600 w (cm"') 800 0 n. (10 6 20 8 cm -3' A ri A Y123 BI2212 B12212(Ni) Y123(Ni) Y123(Ni) film T Y123(Zn) film• Y124(Zn) 10 12 Fig. 52 Tc plotted a function of in the Cu02 planes determined by infrared spectroscopy for pure YBa2Cu307_{ (open triangle) and Bi2Sr2CaCu208+« (open square) single crystal, Ni-doped Bi2Sr2CaCu208+5 single crystal(filled star, this work), Ni-doped YBa2Cu307_4 single crystal (filled diamond), Ni-doped YBa2Cu307_{ films (cross),i»'''i98'i99 Zn-doped YBaaCusOT-* films (filled triangles),^^°'i^^ and Zn-doped YBa2Cu408 single crystals (filled circles).!"! The solid curve is the so-called Uemura line."'^'"* Inset: the frequency-dependent superconducting penetration depth Ai(u;) of Nidoped Bi2Sr2CaCu208+« at 20 K. The values of Ai(0) from the sum-rule analysis are indicated by the symbol.

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CHAPTER VII CONCLUSIONS The underlying theme behind this work has been the investigation of the effect of high magnetic field and substitutional doping on optical properties of cuprate superconductors. First, we present the far-infrared properties of YBa2Cu307_ j films in zero and high magnetic fields. Second, we study a variety of specral fimctions of airplane charge dynamics of Y-doped Bi2Sr2CaCu208 and Pr-doped YBa2Cu307_j single crystals at doping level ranging from heavily underdoped to nearly optimally doped. Third, the afe-plane anisotropy has been excimined on untwinned Pb-doped Bi2Sr2CaCu208+j single crystal above and below Tc, and compared to previous pure Bi2Sr2CaCu208.^*'^''^^ Forth, we discuss the effect of iodine intercalation on the abplane optical response of Bi2Sr2CaCu208+«. FincJly, the a6-plane optical spectra of Ni-doped Bi2Sr2CaCu208+5 have been investigated. For the first issue, we have shown that the reflectance and transmittance spectra of YBa2Cu307_i films as a function and temperature and applied magnetic field. The temperature dependence of zero-field data are consistent with a two-component dielectric response, with the free carriers component condensing to form the superfluid below Tc. However, when varying the magnetic field (with H perpendicular to the ab plane and with unpoleirized light) at low temperatures, the conductivity spectrum shows no discernible field dependence. This observation differs from other previous far-infr
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166 Regarding the evolution of afe-plane charge dynamics from underto optimallydoped regimes, we have focused on the low-frequency optical conductivity and spectr
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167 Bi2Sr2CaCu208.^°^'^*^ Both the one-component and two-component analyses have been employed to the afr-plane optical data, which suggest the normal-state infrared einisotropy of Pb-doped sample originates not only from the mass einisotropy, but also from the scattering rate
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168 Finally, we have investigated the a6-plane opticcd reflectance of Ni-doped Bi2Sr2CaCu208+6. Through Ni substitution, the optical conductivity shows a broad peak at about 400 cm~\ which grows in intensity cind shifts to lower frequency as the temperature is reduced. We suggest that this peculiar low-frequency feature is associated with the significant disorder induced by Ni impurities. Analysis of the conductivity within the framework of the two-component and the one-component pictures indicates that the main effect of Ni substitution is to increase impurity scattering rate. There is no evidence of a rapid drop in the free-carrier scattering rate near Tc. An estimate of the low-frequency spectral weight shows that Ni reduces the carrier density in the Cu02 plane: each Ni removes one ccirrier. Below a sum-rule evaluation finds the superconducting condensate contains about a fifth of the total doping-induced, or two thirds of the free-carrier oscillator strength in the normal state. The strength of the condensate is horizontadly offset from the Uemura line, with a smaller superfluid density than implied by TcThis decreased superfluid density in the Cu02 pl«ine could be connected with the effect of impurity-induced disorder.

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APPENDIX A STRUCTURE AND PHYSICAL PROPERTIES OF A NEW 1:1 CATION-RADICAL SALT, C-(BEDT-TTF)PF6 Introduction Cation-radical salts of the organic donor molecule bis(ethylenedithio)tetrathiafulvalene (BEDT-TTF) have been of great interest since the 1983 report of superconductivity in the salt (BEDT-TTF)2Re04.^°^ At the time, BEDT-TTF was only the second molecule known to form the basis of organic superconductors. BEDT-TTF remains the most important organic donor molecule used in the preparation of new superconducting organic solids with over 50 known superconductors now reported.^"* Currently, the BEDT-TTF salt with the highest superconducting transition temperature is K-(BEDT-TTF)2Cu[N(CN)2]Cl where Tc = 12.8 K under a pressure of 0.3 kbar.2°5 Most conducting and superconducting cation-radical salts in the BEDT-TTF family form with a 2:1 donor:anion stoichiometry with monovalent anions. In the 2:1 salts, the electronic band structure can be thought of as quarter-filled hole-like when considering one BEDT-TTF molecule as the basis unit. In cases where the BEDT-TTF molecules are dimerized, the conduction band is split into two parts resulting in a one-half filled band. While the most conMnonly studied organic cation-radical salts are those where the formal oxidation state of the donor is -f 1/2, other oxidation states of BEDT-TTF are known. In fact, cation-radical salts of BEDT-TTF with oxidation states as high as +2 have been isolated, showing that high-oxidation state salts of BEDT-TTF are stable.^o^ an effort to prepare BEDT-TTF cation-radical salts 169

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170 with differing degrees of band filling, we axe currently pursuing additional examples of high oxidation-state cation-radical salts. The title compound, C-(BEDT-TTF)PF6, is a new cation-radical salt with BEDT-TTF in the -|-1 oxidation state. There are several other known BEDT-TTFrPFe salts including the 2:1 salts a-(BEDT-TTF)2PF6,2°^ ^-(BEDT-TTF)2PF6,208 7-(BEDT-TTF)2PF6,2°9 C-(BEDT-TTF)2PF6-C4H802,2" and (BEDT-TTF)2PF6-ClCH2COC1.2ii Previously reported 1:1 phases include a monocUnic (BEDT-TTF)PF6 phase,203 ^-(BEDT-TTF)PF6,2^^ c-(BEDTTTF)PF6,2i3 (BEDT-TTF)PF6-l/2CH2Cl22^* and (BEDT-TTF)PF6-l/2THF.2ii An interesting aspect of the structure of the new phase reported here is that there is one BEDT-TTF ion per unit cell, resulting in a donor ion network made up of discrete BEDT-TTF monocations with significciut intermoleculcir interactions. In this article, we report the X-ray crystal structure and the treinsport, optical and magnetic properties of C-(BEDT-TTF)PF6. At room temperature the material is a semiconductor exhibiting charge localization due to Mott-Hubbard type interactions. At lower temperatures, two phase transitions are observed. Near 250 K there is a structural transition related to ordering of the cmions. There is also a magnetic phase transition near 40 K that is probably of spin-Peierls origin. Experimental Section MatericJ synthesis BEDT-TTF was prepared following the procedure described by Larsen and Lenoir.2^^ BEDT-TTF (7 mg) was placed in the working electrode arm of a twoelectrode H-cell containing a total of 33 ml of 1.0 xlO"^ M tetrabutylammonium hexafluorophosphate in 10 % CS2/CH2CI2. A constant current density of 1.5 fiA/cw?

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171 was maintained at room temperature between the platinum working and counter electrodes that were separated by two glass frits. Small blawJc needles and plates were obtained upon harvesting after 10 days. C-(BEDT-TTF)PF6 was not obtained if the solvents were degcissed before use. When the solvents were degassed and distilled, other 1:1 phases, ^-(BEDT-TTF)PF62^2 ^nd e-(BEDT-TTF)PF62^^ predominated. We speculate that dissolved oxygen is necessary to form the C-(BEDT-TTF)PF6 phase. The highest yields of C-(BEDT-TTF)PF6 resulted when solvents were used as received from the vendor. X-rav crvstal analvsis Data were collected at room temperature and at 173 K on a Siemens SMART PLATFORM equipped with a CCD area detector, and a graphite monochromator utilizing MoK^ radiation (wavelength = 0.71073 A), and an LN2 Siemens low temperature device. Crystals were mounted on glass fibers using epoxy resin for the room temperature crystal and Paratone N oil for the low temperature crystal. Cell parameters were refined using the entire data set. A hemisphere of data (1321 frames) was collected using the w-scan method (0.3° frame width). The first 50 frames were remeasured at the end of data collection to monitor instrument and crystal stability (maximum correction on I was < 1 %). Psi scan absorption corrections were applied based on the entire data set. Both structures were solved by the Direct Methods in SHELXTLS,'^^^ and refined using full matrix least squares on F^. The non-H atoms were refined with anisotropic thermal parameters. All of the H atoms were include in the final cycle of refinement and refined without constraints. The PF^ unit is found to be disordered in the room temperature structure and ordered in the low temperature structure. Two sets of three F atoms (PF^ is located on a center of inversion) were refined and the

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172 occupation factor of the major part refined to 0.69(2), and consequently the minor has an occupation factor of 0.31(2). Transport techniques The temperature-dependent (180-294 K) four-probe resistance was measured using an ac phase-sensitive technique. Needle-shaped crystals (typically 1.0 x 0.13 x 0.04 nmi^) were measured in this study. Ncirrow gauge (0.02 mm diameter) gold wires were affixed to the crystal under a microscope using fast-drying gold p
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173 for the infrared studies. The initial reflectance reference w«is an aluminum mirror. In order to correct for size differences between sample and reference and to compensate for scattering losses, all samples were coated with a thin alimiiinimi layer after the optical measurements were finished. The final corrected reflectcince was obtained by ratioing the initial reflectance (no coating) to the reflectance of the coated Seimple, then multiplying the ratio by the reflectance of aluminum. After the reflectance spectra were meaisured, the optical properties were determined by KramersKronig analysis.^" Because an extremely large frequency region was covered, Kramiers-Kronig analysis should provide reasonably accurate values for the optical constants. To perform these transformations one needs to extrapolate the reflectance at both low and high frequencies. At very low frequencies the reflectance was assumed constant. Between the highest-frequency data point and 10^ cm~\ the reflectance was cissumed to follow a power law of a;~^ ; beyond this frequency range a free-electron-like behavior of u;"^ was used. Magnetic measurements The temperature dependence of the magnetic susceptibility was obtained from magnetization measurements in a standard coumaerdal SQUID magnetometer. The samples were a set of randomly oriented single crystals with a total mass of 5.9 mg (sample 1) and 13.2 mg (sample 2). A gelcap and a plastic straw were used as the sample holder during the meeisurements. Samples 1 and 2 were zero field cooled to 2 K before a measuring field of 100 G or 1.0 kG was applied. Each data set was taken while warming the scimple from the lowest temperature. The bax:kgroimd signals arising from the gelcap eind straw were measured independently cind subtracted from the results. Electron spin resonance (ESR) spectra were recorded between 4 and 298 K using a Bruker ER-200 spectrometer equipped with an Oxford Instruments ITC 503 tern-

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174 perature controller and ESR 900 flow cryostat. A C-(BEDT-TTF)PF6 single crystal (1.25 X 1.0 X 0.06 mm') was selected and mounted on a cut edge of a quartz rod; rotation was achieved using a homebuilt goniometer. The sample was first oriented vertically in the microwave cavity. The 0° and 90° orientations corresponded to the parallel and perpendictdar cilignments, respectively, of the crystal plaaie normal (c*) with respect to the static magnetic field. On the second nm, the sample was oriented horizontally in the microwave cavity, that is, the microwave electric field is parallel to the crystal plane {ab plane), and the static magnetic field perpendicular to the c* axis. The temperature-dependent electron spin resoncince data were obtained at 9.26 GHz with 100 kHz field modulation. Results Crvstal structure C-(BEDT-TTF)PF6 crystallizes in the triclinic system PI. Crystallographic data for both room temperature cind 173 K axe presented in Table A-1. Atomic coordinates and equivalent isotropic displacement parameters are listed in Table A-2. Like many BEDT-TTF cation-radical s«ilts, two-dimensional sheets of the cationradiccds are sepcirated by sheets of the counterions. The anion and cation sheets eire oriented parallel to the ab plcine shown in Fig. A-1. A consequence of the low crystal symmetry is that the principal molecular axes of the BEDT-TTF ion do not correspond with any of the crystallographic axes. In the low-temperature crystal structure, the long axis of the BEDT-TTF cation forms angles of 74", 34°, and 56° with the a, 6, and c axes, respectively. At room temperature, the PF^ ion is located on a center of inversion and is rotationcJly disordered. The structure was refined with two sets of three F atoms having occupation factors of 0.69(2) and 0.31(2). The PF^ ions cire ordered in the low-temperature structure.

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175 Table A-1. Crystallographic data for C-(BEDT-TTF)PF6 at 298 and at 173 K. 298 K 173 K a(A) 6.2793(1) 6.2293(1) b(A) 7.3680(1) 7.2633(2) c(A) 9.9006(1) 9.8662(2) 92.542(1) 93.898(1) 93.255(1) 93.592(1) 7° 98.763(1) 97.914(1) Vol{k^) 451.33(1) 439.95(2) dca/c, g cm"^ 1.949 1.999 Empiriceil formula CioH8S8(PF)6 CioH8S8(PF)6 Formula wt, g 529.61 529.61 Crystal system Triclinic Triclinic Space group Pi PI Z 1 1 F(OOO), electrons 265 265 Crystal size (mm^) 0.30x0.21x0.14 0.28x0.21x0.15 Radiation, wavelength (A) Mo-K«, 0.71073 Mode w-scan Scan width and rate 0.3° /frame and 30 sec. /frame 29 range, deg. 3-55 3-55 Total reflections measured 3324 3274 Unique reflections 1806 1773 Absorption coeff. /i(Mo-Ka),mm~^ 1.129 1.158 S, Goodness-of-fit 1.086 1.113

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176 Table A-2. Atomic coordinates (xlO^) and equivalent isotropic displacement parameters (A^ x 10^) for C-(BEDT-TTF)PF6 at 298 and 173 K. Ueq is defined as one-third of the trace of the orthogonalized Uy tensor. Atom X 298 K y z Ueq X 173 K y z Ueq S(l) 1459(1) 6637(1) 8422(1) 41(1) 1424(1) 6620(1) 8421(1) 21(1] S(2) -2455(1) 6782(1) 9834(1) 42(1) -2503(1) 6808(1) 9847(1) 21(i; S(3) 1264(1) 9988(1) 6947(1) 48(1) 1121(1) 9944(1) 6915(1) 23(1] S(4) -3544(1) 10082(1) 8529(1) 48(1) -3730(1) 10068(1) 8511(1) 24(1] C(l) -215(3) 5734(3) 9621(2) 36(1) -230(3) 5734(3) 9632(2) 19(1] C(2) 87(3) 8468(3) 8088(2) 34(1) -9(3) 8456(3) 8080(2) 18(1] C(3) -1744(3) 8523(3) 8742(2) 35(1) -1850(3) 8527(3) 8735(2) 18(1] C(4) -658(4) 11564(3) 6727(2) 43(1) -828(3) 11577(3) 6750(2) 21(1] C(5) -2974(4) 10698(3) 6823(2) 43(1) -3153(3) 10684(3) 6812(2) 21(1] P 5000 5000 5000 39(1) 5000 5000 5000 19(1) F(l) 3532(16) 6419(10) 5481(8) 99(2) 3651(3) 6559(2) 5579(2) 39(1) F(2) 3395(7) 3315(7) 5419(11) 103(2) 3274(3) 3389(2) 5477(2) 48(1) F(3) 6169(16) 5087(7) 6448(5) 112(3) 3660(3) 4908(2) 3562(2) 50(1) F(l') 4090(34) 6685(17) 5597(19) 91(5) F(2') 4047(31) 3918(19) 6206(15) 99(6) F(3') 2848(17) 4500(23) 4185(22) 143(6) For anisotropic atoms, the U value is Ueq, calculated as Ueq = 1/3 X)i Ej UyafaJAy where Ay is the dot product of the ith and jth direct space unit cell vectors. Figure A-2 shows the molecular arrangement within the BEDT-TTF sheets. Along the 6-axis, molecides appear to stack face-to-face, but because the molecules

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177 are slipped relative to each other, overlap is poor. The closest intennolecular nonbonding orbital interactions are the nearly side-by-side contacts between outer-ring sulfur atoms on adjacent molecules along the a-axis. The S-S contacts are 3.525 A at room temperature, decreasing to 3.470 A at 173 K. There is cJso a short S-S contact along the ab direction between the outer-ring sulfur atoms at opposite ends of the molecules. Additionally, a number of nonbonding interactions aire also observed involving the BEDT-TTF donors and PF^ ions at both room temperature and 173 K. The crystal packing of the monocation salt ^-(BEDT-TTF)PF6 closely resembles that in <5-(BEDT-TTF)PF6^^^ where two-dimensional sheets of donor molecules are also separated by layers of PF^ counterions. In C-(BEDT-TTF)PF6, the donor ion sheets are comprised of discrete BEDT-TTF"*" monomers, while in the ^-phase there is increased face-to-face overlap and the donor ions are strongly dimerized. At room temperature,
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178 high T and 0.23 eV at low T. The smaller Ea at low temperature is probably due to subtle structural changes within the BEDT-TTF planes that accompiiny ordering of the PFg" anions. As previously mentioned, three other examples of BEDT-TTF cation-radical salts have the seime coimterion and stoichiometry as (^-(BEDT-TTF)PF6. There are no reports of conductivity mecisurements in those salts. On the other hand, conductivity has been measured in the 2:1 salts, a-(BEDT-TTF)2PF6 and ^-(BEDT-TTF)2PF6. The a phase is a onedimensional semiconductor at room temperature with a ~ 0.1 n-^cm-^ and an activation energy of ~ 0.05 eV.^'^^ /3-(BEDT-TTF)2PF6 is metallic with cr ~ 10 n~^cm~^ near room temperature and shows the meted-insulator transition at 297 K.2°8 The conductivity of C-(BEDT-TTF)PF6 is comparable to that of other 1:1 organic conductors with integer charge on the molecules. For example, the electrictd conductivities of the alkali-TCNQ (TCNQ=tetracyanoquinodimethan) stdts exhibit semiconducting behavior;
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179 parallel to the a-axis, the spectrum displays a series of narrow structures associated with molecular vibrations at low frequencies and a broad maximum peak along with several weak features from electronic transitions at higher frequencies. In contrast, perpendicular to the a-axis, the reflectance is low (~ 5%) and almost dispersionless. The real pait of the conductivity
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180 e{u) = ei(a;)+te2(w)] from the near-infraxed to ultraviolet regions to a sxun of Lorentz oscillators is also shown. The model dielectric function is^° = E 2 + ^«>' (A-2) where Wpj, ajy, and 7j are the oscillator strength, center frequency, and scattering rate of the j*^ transition and Cqo represents the other higher frequency contributions to the dielectric function. The parameters obtained for our sample are listed in Table A-3. The results for the fit «ire compared to ei{u>) in Fig. A-6. Table A-3. Parameters of Lorentz fit to the a-axis reflectcince of ^-(BEDTTTF)PF6, see Fig. A-6. Oscillators Upj Uj 7^ ( cm-i) ( cm-i) ( cm-i) 1 9179 7990 1605 2 4713 9310 1793 3 1420 17500 852 4 2570 20860 1856 5 7700 23390 3928 6 14116 32900 3983 Coo = 2.05 Additional information about the electronic structure of C-(BEDT-TTF)PF6 can be extracted from the oscillator strength sirni rule.^° The effective number of electrons pairticipating in opticcd transitions for energies less than hw is given by 0

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181 where m* is the effective mass of the cairiers, m the free-electron mass, and VctU the unit cell volume. A plot of this function vs. frequency is shown in Fig. A-7. In the a-direction, {m/m*)Ncff is small until 5000-6000 cm~\ where it rises very rapidly and begins to level off, emd then rises again above the onset of the high-frequency electronic bands. From the plateau value (~ 0.47) of {m/m*)Ncf[, assuming that the carrier density is equal to the number density of BEDT-TTF"*" molecules, we estimate m* = 2.13 m. In the polarization perpendicular to the a-direction, (m/m*)iVeff is close to zero in the infrared but rises at higher frequencies. The anisotropy ratio of the effective mass, m^/m|| = 4.9, is larger than the corresponding values in metallic BEDT-TTF salts, where values of 3.5, 2.1 and 1.4 are reported for /?-(BEDT-TTF)2l3,^^' B{BEDT-TTF)2l3^^* and K-(BEDT-TTF)2l3,"^ respectively. Temperature dependence in the far infrared . To compare the high-temperature and low-temperature phases in C-(BEDT-TTF)PF6, Fig. A-8 shows the far infrared conductivity spectra for both polarizations at several temperatures. We observe no significant temperature variation perpendiculax to the a-axis, but the character of the frequency-dependent conductivities along the a-axis is a strong function of temperature, indicating that important changes occur in the lattice and electronic structures as the result of the 250 K PF^ order /disorder transition. Magnetic properties Magnetic susceptibility . The temperature dependence of the magnetic susceptibility of sample 1 is plotted in Fig. A-9. Similar results were obtained for sample 2. After correction for the core diamagnetic component calculated using Pascal's constants (Xcore = 1-4 x 10""* ± 0.2 x 10"'* emu/mol),^^^ a room-temperature susceptibility of 3.4 X lO""* emu/mol was determined. Over the entire temperature region, the static susceptibility at first decreases gradually from room temperature to 200 K, and then shows Uttle variation with temperature down to 40 K, while einother

PAGE 190

182 weaJcer change of slope is observed at 130 K. Below 40 K, X falls off rapidly. However, at temperatures lower than 10 K, the data are dominated by a Curie-like tail, presumably arising from magnetic defects or impurities. This region is shown on an expanded scale in the inset. ESR spectra . The X-band ESR signal of C-(BEDT-TTF)PF6 was measured as a fimction of orientation and temperature. Figure A10 shows the temperatiire dependence of the peadc-to-peak derivative ESR linewidths (AH), recorded with the microwave field parallel, and the static magnetic field aligned perpendicular, to the face of the plate-like crystals. The maximum peak-to-peak linewidth at room temperature is 9.4 G and then AH decreases nearly monotonically to about 4.0 G at 100 K. Below 100 K the linewidth decreases rapidly to a minimum of 1.4 G near 30 K, at which point there is no ESR signal detected as the temperature was lowered further. The loss of the ESR intensity is observed in all cryst«Jlographic directions at T < 30 K. The g-value of C-(BEDT-TTF)PF6 is ahnost temperature independent with deviations of only ±0.002 from 2.010 between 300 and 30 K. Discussion Cation-radical salts are a clciss of compounds which display many interesting aspects of low-dimensional physics. It is generally accepted that the chemical identity of the donor cation and the stoichiometry of the salts determines the population of the conduction band. In these materials, interactions involving unpaired electrons in the highest occupied molecular orbital (HOMO) have especially import«int consequences. The tight-binding model is often used to obtain a band structure from the overlap integrals of molecular orbitals, while the extended Hubbard model describes the transfer integr
PAGE 191

183 there is one unpaired electron on each BEDT-TTF molecule. Because of the strong electron-electron Coulomb interaction the electrons eire imlikely to doubly occupy sites. Hence, the tight-binding band is split into two bands, separated by a wide gap on the order of U. Electronically, they are often referred to as Mott-Hubb
PAGE 192

184 where no is the number density of dimers eind a the intradimer sp
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185 despite the very short S-S contact. This resvilt is a reminder of the importance of discussing the strength of the intermolecular interactions, as far as the transport properties are concerned, on the basis of /^homo-HOMO interaction energies and not solely on the basis of short S-S contacts. The Ccdculation suggests that the electrons on the BEDT-TTF donors are mainly confined to the stacks formed along the a axis, which is consistent with the observed opticcd properties. However, the 6-axis /? energy is only about two times smaller than that cdong the a direction. This would favor the aiTeingement of BEDT-TTF units as a series of step chains along the a-axis coupled weakly along the 6-axis. The fact that the interactions are not negligible is clear when looking at the dispersion of the HOMO band. Although the band structure heis less meaning in a loccdized system, it gives an idea of the strength of the interactions in the lattice. For metallic BEDT-TTF salts, the total dispersion of the HOMO bands is typically around 1.2 eV which is not far from the value of 0.75 eV calculated for C-(BEDT-TTF)PF6. With such a bandwidth for a single band system, the salt coidd have well been a metal. Thus, the semiconducting behavior of C-(BEDT-TTF)PF6 must be from the strong electron-electron correlation effects. Vibrational spectra There are three different phenomena seen in the infrared spectral region, where the vibrational features of the C-(BEDT-TTF)PF6 crystal occur. First, there is strong activation of the Ag modes of the BEDT-TTF molecule for light polarized along the a axis. Second, there is interesting temperature dependence to the PFe vibrations at ~ 556 eind 883 cm~^. Third, we observe many weaker phonon structures for polarization perpendicular to the a-axis that seem to fit quite well into the pattern of the ordinary infrared-active modes. The C-H stretching Bi„(i/26) is resolved at ~ 2920 cm . The features near 1445 and 1411 cm~^ should correspond to C=C stretching Biu{v27) and C-H bending B2tt(i/45)More than likely there is another C-H bending Buii^i) at ~

PAGE 194

186 1379 cm~^. There is a band at ~ 1283 cm~^ which is related to complex C-S motion Bitt(i'29). The feature centered ciround 500 cm~^ is probably C-S bending Bi„(i/34). We discuss the first cind second of these effects in the following sections. Electron-phonon coupling Room — temperature data . Among the most prominent and interesting spectral features of BEDT-TTF charge-transfer stJts are the in-plane Ag modes of the BEDT-TTF molecule, activated by coupling to the charge-transfer excitations. "^''"^^^ Thirteen out of the expected seventeen Ag modes cire observed in the a-axis specivwca. of C-(BEDT-TTF)PF6, most with relatively strong intensity. This interaction has been previously observed in the infraired spectra of many other conducting and semiconducting BEDT-TTF salts.233.236-24i r^^ie features have been interpreted with the help of the microscopic theories of electron-molecultirvibration (EMV) linear interactions in the one-dimensional organic solid state given by Rice and coworkers, the phase phonon theory"^*^ and dimer models.^^"'"^^^ Consequently, we analyze the conductivity spectrum of C-(BEDT-TTF)PF6 in terms of an isolated, half-filled, dimer model.220 In this model, the frequencydependent conductivity is where o is the dimer separation, N is the number of dimers per unit cell, and is the volume of the unit cell. The quantity D{u) is the phonon propagator ^M = E 2 > (A-7)

PAGE 195

187 with An the dimensionless electronphonon coupling constant, cJn the unperturbed frequency, and 7„ the phonon linewidth for the nth Ag mode. is the reduced electronic polarizability, m 1/2 0(u;) = ^2 , (A-8) where ujct is frequency and 7e is the linewidth of the electronic charge transfer excitation. Taking the zero frequency Umit of the above expression, we find The dimensionless coupHng constants axe written as A = V(0)^. (A-10) It is the gn which are the fimdamental microscopic electron-molecularvibration coupling constants. Interaction of the Ag phonon mode with the charge transfer excitation causes the resonance frequency of the vibration to be shifted to lower frequency from its unperturbed position in an isolated moleciile. Within the isolated dimer model, we can calculate where A and B are constants, relating to the dimensions of the unit cell and the electronic parameters, respectively. Thus, by fitting a sum of Lorentzian oscillators to this function, we can obtain the unperturbed frequencies of each Ag mode.^^^

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188 A fit of this model to the C-(BEDT-TTF)PF6 data is shown in Fig. A-11. The structured parameters used in the Ccdculation were the separation between the BEDTTTF molecules a = 3.524 A and the unit-cell volume KeU = 451 A^. The fitted parameters for the cheirge-trtinsfer band axe a transfer integral, t = 1700 cm~\ and an effective Cotdomb repulsion, Ueff = 6620 cm~^. The chargetransfer energy and electronic linewidth are ujct = 7990 cm~* and 7e = 1900 cm~^ The experimental values for the unperturbed phonon frequencies a;„, EMV coupling constants and dimensionless electron-phonon coupling constants An are listed in Table A-4. As shown in Fig. A-11 and Table A-4 we have assigned the highest-frequency EMV vibrational features at ~ 2986 and 2934 cm~^ to the totally symmetric C-H stretching BEDT-TTF motion: u\ and 1/2. The strongest interaction between the electronic system and the intramolecular Ag vibrations is memifested by the modes in the 1400cm~^ range. The peak at ~ 1447 cm"' is probably connected with the ring C=C stretching ^5(1/3). The bands close to 1420, 1412, and 1360 cm"' are due to EMV coupling of the Ag mode which involves the central C=C stretching (1/4). It should be noted that the calculated EMV coupling constants for these modes are the greatest of any Ag mode. The mode near 1287 cm"' is believed to be either H-C-H bending Ag{v5) or C-C-H bending Ag{i'e). The bands that are of unambiguous origin from 900 to 600 cm"' are the two C-S stretching modes Ag{i/io, uu) at ~ 878 and 636 cm"'. The next largest features are in the group near 500 cm"', which have been assigned to the C-S stretching Ag{ui2) and which appear as a triple mode at ~ 502, 494, and 485 cm"'. Certaiidy Ag{i/i2) is calculated to have the second-largest EMV coupling constant. The remaining mode at ~ 452 cm"' is the C-S stretching Ag{ui3). Low temperatiire data . As mentioned above, the far infrared spectrum of (BEDT-TTF)PF6 has several strongly-temperature-dependent vibrational features polarized along the a-axis. Some of these modes are readily understood as arising

PAGE 197

189 Table A-4. Electron-molecular-vibration coupling parameters for ^-(BEDTTTF)PF6. gn A„ (cm-^) ( cm-*) 2986 140 0.001 2934 145 0.001 1452 300 0.009 1425 235 0.006 1420 350 0.013 1385 450 0.022 1290 180 0.004 878 100 0.002 636 100 0.002 502 250 0.020 494 130 0.005 485 90 0.003 452 155 0.008 Total 0.096 "Obtained from plot of Re[l/
PAGE 198

190 the exterior ring deformation (1/15) and interior ring deformation (t'le), respectively. The oscillator strengths of these lowest-frequency Ag modes are plotted in Fig. A-12 (a) versus the temperature. These data have been normalized with respect to their 25 K value. As can been seen, the spectral weight of the 478 and 300 cm~^ modes cheinges in a relatively gradual cind continuous manner with increasing temperature. Above 200 K, both decrease to zero. In contrast, the 142 cm~^ mode displays a stronger temperature v
PAGE 199

191 Anion ordering transition We will now turn to a discussion on the nature of the phase transitions in ^(BEDT-TTF)PF6. The high temperature transition, observed near 250 K in dc conductivity and magnetic susceptibility measurements, is a structural transition associated with ordering of the PF^ ions within the ainion sheet. Optical
PAGE 200

192 seen at ~ 556 and 883 cm~^ for both polarizations in Figs. A-4 and A-8 are the PF^ion bending VilFi^) and stretching i^3(Fi«) modes. The temperature dependence of the center frequency, linewidth and oscillator strength of the bending mode (from fits to Lorentz oscillators) are displayed in Fig. A-13. Errors in the the parameters are ± 5 %. We note two effects: (1) A reduction of 7 (decrease in the dcimping) as the temperature of the sample is decreased from 300 to 200 K, with some saturation in 7 below 200 K, and (2) there is a splitting of the modes for both polarizations as the temperature is lowered. These figures clearly indicate that the PFg anions freeze into position below the order /disorder structural transition. The changes in the electron-phonon coupling between the highcind lowtemperature phases has already been discussed. This interaction is fundamentally related to changes in the lattice distortion cind electronic configuration. As already shown in Fig. A-8(a), the strong triple Ag mode nccir 500 cm~^ disappears upon cooling from room temperature to 200 K and is replaced by a single strong mode. This result indicates that there is a chcinge of the environment of the BEDT-TTF molecules in the low-temperature phase, directly connected with the ordering of the PF^ counterions. This change may be attributed to the reduced distance between the BEDT-TTF donors along the crystallographic a-axis in the low-temperature structure. The Ag intramolecular vibration spectra are also useful for investigating the dynsimic aspects of the phase transition. In particulcir, they allow study of the amplitude of the charge-density distortion or lattice dimerization: a strong lattice distortion results in a charge density wave with a large amplitude and consequently strong activation of the vibrational modes of proper symmetry; a wecik or non-existent lattice distortion resxilts in little or no activation.

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1 193 The temperature dependence of the order parameter, A, rather than the eflFective lattice dimerization, is actually the more fundamental qucintity with which to probe the nature of the charge-density wave. Bozio et al?*^'^** have discussed the relationship between the Ag phonon mode oscillator strengths and the order parameter. They find the oscillator strength of the totally symmetric vibrational modes to be proportional to A'^. We have analyzed the optical data presented in Fig, A-12 (a) along these Unes. The solid line in Fig. A-10 (a) shows a phenomenological curve iVeff ^ ^p(r) No u;2(o) where we have used A(T) as the temperature-dependence of the (mean-field) BCS order parameter. This assumption gives a nearly constant A(r) at T -C Tc] near Tc, A(r) drops to zero with a {l-T/Tc)^/^ behavior. Taking Tc = 250 K, the normalized oscillator strength of the three lowest-frequency Ag beinds agrees with this expression. We can conclude from the gradual variation of the integrated spectral intensity of the 478, 300, and 142 cm"^ Ag modes in C-(BEDT-TTF)PF6 with temperature that the order pareimeter of the phase transition changes gradually with temperature in this compound. The previously discussed chcinges in the dc conductivity and magnetic susceptibility were also gradual in this temperature range. Consequently, this hightemperature trcinsition in C-(BEDT-TTF)PF6 can be described as a second-order process. Magnetic phaae transition The most striking feature in the magnetic susceptibility data of Fig. A-9 is the exponential drop in susceptibility toward zero at T < 40 K. The slight increase of the X value at T < 10 K obeys the Curie law and is believed to be extrinsic in origin. For reasons discussed below, we have treated the 40 K drop in susceptibility as a A(r) A(0) (A-12)

PAGE 202

194 spin-Peierls transition. The general approach to ancilysis the data will be similar to those"^*^"^^^ that have followed the Hartree-Fock predictions of Bulaevskii,^^^ with additioncd input from Pytte.^^^ The magnetic transition temperature, Tgp, is defined by the kink in the susceptibility vs. temperature plot. The finite energy gap is assimaed to have the usual BCS temperature dependence and in the ground state it is given by A(0) = 1.76kBTsp (A-13) We cissume that J = 4Tsp, since the expression provided by Bulaevksii^^^ is valid for T/J < 0.25. Below Tgp two alternating J's[Ji^2{T)] are formed and expressed as: Ji,2(r) = J[l ± S{T)] (A-14) According to the mean-field theory of Pytte^^' the relationship between ^(r) and the excitation energy gap A(r) at temperature T is foimd from m = ^ (A-15) where the vcdue of p is 1.637. The above choices define the parameters needed for obtaining a theoretical fitting for X(r < Tsp). The estimate of X(r8p) is multiplied by a factor to sc
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195 Table A-5. Values of the fitting parameters to the static susceptibility of C-(BEDT-TTF)PF6, see Fig. A-9. Sample Tsp(K) A(0)(K) J(K) mult. X(0)(emu/mol) C(emu K/mol) 1 in IkG 40 70 160 0.12 7.5 xlO-5 7 xlO-5 2 in IkG 43 76 172 0.10 1.4 xlO"* 4 xlO-* 2 in 100 G 43 76 172 0.18 1.9 xlO"" 6 xlO-"* As the temperature is lowered in a quasi one-dimensional Heisenberg antiferromagnet there is a competition between a three-dimensional ordered antiferromagnetic state and the spin-Peierls ground state. Based on magnetic susceptibility data jdone, it can be difficult to distinguish between the two ground states. Although X for an ordered antiferromagnet is anisotropic, in powder scimples X rapidly decreases below the ordering temperature for both antiferromagnetic and spin-Peierls states. However the temperature dependence of X is different in the two cases below Tap, and the susceptibility of C-(BEDT-TTF)PF6 is nicely fit by a spin-Peierls model, as seen in Fig. A-9. The ESR behavior is also consistent with a spin-Peierls transition. The ESR linewidth decreases as the temperature is lowered toward Tgp, below which the X-band signal rapidly disappears and is no longer present at 30 K. On the other hand, for systems approaching antiferromagnetic order, the ESR behavior is expected to be different. Pretransitional antiferromagnetic fluctuations cause a rapid divergence of the ESR linewidth as the temperature decreases toward the Neel temperature Tn and the ESR signal becomes too broad to observe just above the ordering transition. Below Tn, antiferromagnetic resonance modes, if observable, will be far removed from the g = 2 lines seen above the transition. In the spin-Peierls case, dimerization proceeds progressively below Tgp, resulting eventually in a nonmagnetic state. The system remains paramagnetic just below Tgp until the magnetic gap becomes too large as the

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196 temperature is decre«ised further. The observation of a narrow ESR line at and just below the transition temperature is consistent with the spin-Peierls assignment. Unlike antiferromagnetic ordering, the spin-Peierls transition is a structural transition. Qualitatively, the spin-Peierls transition cein be described as a magnetoelastic transition whereby onedimensional spin chains couple to a three-dimensional phonon, resulting in the spin-lattice dimerization proceeding continuously and progressively below the transition temperature. While the dimerization should be seen below Tsp, precursive lattice softening is often observed at temperature well above Tsp. Precursive eflFects were seen in the first reported spin-Peierls system, the meted bisdithiolene complexes of tetrathiafulvalene (TTF),^''^'^''^ (TTF)Cu(S2C2(CF3)2)2 and (TTF)Au(S2C2(CF3)2)2 which have Tsp of 12 K and 2.1 K, respectively. A diflFuse Xray study of (TTF)Cu(S2C2(CF3)2)2 above Tsp shows the persistence, up to at least 225 K, of enhanced scattering at the position of the new Bragg peeiks seen below TspThis scattering was foimd to be approximately isotropic in fc-space, indicating that the implied precursive lattice softening is fully three-dimensional. The apparently fortuitous existence of this soft phonon mode at the wave vector {2kf) appropriate for lattice dimerization facilitates the occurrence of the spin-Peierls transition. We have not performed structural analyses below 40 K on C-(BEDT-TTF)PF6, but the appearance of new intermolecular vibrational modes at temperature above Tap are evidence for three-dimensional lattice softening of a lattice mode compatible with spin-Peierls dimerization. Three new lattice modes near 93, 85, and 82 cm~^ become observable at temperatures above Tgp and increase oscillator strength as the temperature is lowered. The temperature dependence of the vibrational intensities axe shown in Fig. A-12 (b). Their appearance is reminiscent of precursor eflFects seen in other spin-Peierls materials and is consistent with the assignment of the 40 K magnetic trcinsition to a spin-Pederls transition.

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197 Spin-Peierls transition have been observed in several other molecular solids. Some examples include the TCNQ salt MEM(TCNQ)2^'** (MEM is the methyhnorpholinium cation), the cation radical salt (TMTTF)2PF6^^'*~^^^ (TMTTF is tetramethyltetrathiafulvalene), and (BEDT-TTF)2Ag(CN)2.2'*^ In each case a high-temperature structured trcinsition or structural pretransitional fluctuation was observed at temperatures well above Tsp. While the spin-Pderls state is most commonly seen in molecular solids, a spin-Peierls transition was recently discovered in the purely inorganic compound CuGeOs.'^^^'^^^"'^^^ A final point to consider is the role of the Peierls transition in the Hubbard model for a half-filled band. For U = 0, the charge and spin degrees of freedom are unseparated and the Peierls transition opens equad gaps for both the charge and magnetic excitations by means of a lattice distortion at 2kY. As U increases, a new instability appears at 4^;f which is chiefly associated with electron localization and therefore with reduction of the charge degrees of freedom. The 2kY instability remains but becomes more associated with the spin degrees of freedom as U increases, gradually evolving into a spin-Peierls transition for i7 > 1 In the case of C-(BEDT-TTF)PF6, all physical properties demonstrate that this material is a magnetic insulator of the Mott-Hubbard type. In Hght of the large value C/ > t, it would seem then that the charge degrees of freedom are frozen out even at high T, with strong localization of the charge carriers. Then, the spin degrees of freedom are lost at low temperature. Thus, the ground state of C-(BEDT-TTF)PF6 can be considered as a 2ibF spin-Peierls state.

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198 Summaxv In summajy, a new 1:1 cation-radical salt, ^-(BEDT-TTF)PF6, has been synthesized and characterized. Its physical properties demonstrate that this material is a magnetic insulator of the Mott-Hubbard type. From an cmailysis of the frequencydependent optical conductivity we obtain values for the effective on-site Coulomb repulsion t/gff = 0.82 eV, and for the transfer matrix element t = 0.21 eV. ^-(BEDTTTF)PF6 would fall into the intermediated-to-strong Coulomb correlation case because of ?7eff ~ 4f. The a-axis conductivity shows the effects of electron-molecularvibration interaction with a dimensionless electron-phonon coupling constant A*-0.1. Upon comparison of the structured, transport, optical, and magnetic properties of ^-(BEDT-TTF)PF6, it becomes clear that this salt exhibits successive phase transitions. A direct observation of ordering of PF^ anions has been obtained by means of X-ray diffraction measurements at 173 K. The net effect of this order/disorder transition is to reduce the VcJue of the transport activation energy below 250 K eind to cause the magnetic susceptibility to decre«ise in a continuous manner from 300 to 200 K, with a very small discontinuity at 250 K. The optical results showing a splitting of the PF^ bending vibration and the change from a triple to a single Ag mode of BEDT-TTF donor molecule near 500 cm~^ are
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199 precursive three-dimensionaJ softening of the phonon corresponding to the eventual spin-Peierls dimerization. The softening phenomenon facilitates spin-phonon coupling and appears to be associated with a structural treinsition in C-(BEDT-TTF)PF6.

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200 Fig. A-1 View down the a axis of C-(BEDT-TTF)PF6 at room temperature. The dashed lines represent nonbonding interactions. Disorder in the anion network hcis been omitted for clarity.

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201 Fig. A-2 View along the long axis of C-(BEDT-TTF)PF6 showing the packing arrangement of the BEDT-TTF units at room temperature. PFe anions have been removed for clarity. The dashed lines represent S-S distances that are less than the sum of the van der Waals radii.

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202 150 200 250 300 Temperature (K) Fig. A-3 The dc conductivity normalized by its room-temperature value (l.lxlO-'t ± 0.1x10-'' fi-^cm-i) for C-(BEDT-TTF)PF6 as a function of temperature. Inset shows the plot of In (t versus 1000/T.

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203 Photon Energy (eV) 0.1 1 "~i I 1 r-r-| I I 1 1 1 — I — I I I f-(BEDT-TTF)PF6. T = 300 K 100 1000 10000 Frequency (cm~^) Fig. A-4 The room-temperature reflectance of C-(BEDT-TTF)PF6 with light polarized along the a-axis reflectance direction (solid line) and perpendicular (dashed line) to it on the (001) crystal face.

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204 1 000 800 600 400 200 0 100 Photon Energy (eV) 0.1 T 1 — I — I — r-r -I 1 1 1 — TT t-(BEDT-TTF)PF6 T = 300 K E II a E 1 a Frequency (cm ^) Fig. A-5 Frequencydependent conductivity obtained by Kramers-Kronig analysis of the room temperature reflectance of C-{BEDT-TTF)PF6. The conductivity is shown for parallel and perpendicular to the a-axis.

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205 15 1 0 CO Photon Energy (eV) 0.1 1 -I 1 1 T — \ — I — r-T(t-(BEDT-TTF)PF6^ T = 300 K E a Data Fit A 1 J 1/ -5 I I I I 1 1_L. _1 I I I I I L_l_ 1 00 1000 10000 Frequency (cnn~^) Fig. A-6 The real part of the dielectric function (dcished line) obtained by Krcimers-Kronig analysis of the room temperature reflectance of ((BEDT-TTF)PF6 along the a-direction. Lorentz fit to the reflectance data is shown as the solid lines, and the fitting parameters of Eq. A-2 are given in Table A-3.

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206 Photon Energy (eV) 0.0 0.5 1 .0 1.5 2.0 -I 1 \ 1 1 1 1 1 1 r' ' I -I 1 1 1 1 1 1 r C-(BEDT-TTF)PF6 T = 300 K E II a E 1 a 5000 10000 15000 Frequency (cm~^) 20000 Fig. A-7 The result of the partial sum rule analysis for C-(BEDT-TTF)PF6 with polarization parallel and perpendicular to the a-axis, see Eq. A-3.

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207 600 Photon Energy (meV) 40 60 0 20 40 "1 I I I — I — 1 — I — I — I — I — I — I — I — I — I — I — r (a) HBEDT-TTF)PF6 20 60 a 7 400 E o b 200 0 "> I I I I I — I — I — I — 1 — I — I — I — I — I — r (b) E 1 a 25 K 50 K 300 K J , L -A 100 200 300 400 500 0 100 200 300 400 500 600 -1 Frequency (cm ) Fig. A-8 Detailed temperature dependence of the far-infrared conductivities of (-(BEDT-TTF)PF6 for both polarizations. The curves have been offset for clarity.

PAGE 216

208 I 1 I 1 I I I I I I I — 1 — I — I I 1 I 1 I ! I I I I I I I I I 0 50 100 150 200 250 300 Temperature (K) Fig. A-9 The temperature dependence of the magnetic susceptibility of ^(BEDT-TTF)PF6, sample 1. The inset shows solid line as outlined in the text the calculated susceptibility with the parameters given in Table A-5.

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209 10 8 _ <--(BEDT-TTF)PF6 0 -I — I — I — r — ' — ' — ' — ^ — I — ' ^ I I I I I I I I I J I I 1 I I I I I I I I _1 I ' I I I L. 50 100 150 200 250 300 Temperature (K) Fig. A-10 The temperature dependence of the ESR peak-to-peak linewidths for C-(BEDT-TTF)PF6.

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210 0.0 400 Photon Energy (eV) 0.1 0.2 0.3 300 E o T G 200 3^ 100 0 (r-(BEDT-TTF)PF6 Experiment Theory 1 000 E o G 500 3 I I I r~] I I I I CO (cm ^) -I I L. 0 1000 2000 Frequency (cm~^) 3000 Fig. A11 Isolated dimer fit (solid line) to the frequency-dependent conductivity (dashed line) of C-(BEDT-TTF)PF6. Inset shows the conductivity in the range up to 10000 cm"^

PAGE 219

211 1 .2 I — ' — \ — ' — I — ' — I — ' — I — ' r Temperature (K) Fig. A-12 Normalized oscillator strength of (a) three Ag modes, and (b) three lattice modes of C-BEDT-TTF)PF6 vs temperature. The sohd line is a fit using the temperature dependence of the BCS (mean-field) order parameter.

PAGE 220

212 560 I — ' — I — I — ' — I — ' — I — ' — ' — I — ' — ' — ' — ' — I — ' — ' — ' — ' — 1 — I — I — I — >" 555 550 X 4 I E O 0 1 00 50 ~i — I — r — r PFg bending mode ^""^ -•Ell _ El I I I I I I I I I I I I I I I I I I I I I I I I I I I I I (b) _•_ Ell 11 El ^ I I I I I I I I I I I (c) ^ ^ • Ell V ^ ^ _-_ El -J — I I 1 I — I I — 1 1 I I 1 I I I I I I I ™ I I I I I I I I I 0 50 100 150 200 250 300 Tennperature (K) Fig. A-13 The temperature dependence of (a) center frequency wq, (b) line width 7, cind (c) oscillator strength of PFe anion bending mode for two different polfirizations.

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APPENDIX B OPTICAL AND TRANSPORT STUDIES OF Ni(diiiit)2 BASED ORGANIC CONDUCTORS Introduction In 1973, cin organic charge-transfer complex composed of the donor molecule TTF (tetrathiafulvalene) and the acceptor molecule TCNQ (7,7,8,8-tetracyano-pquinodimethane) was synthesized and found to display metallic-like electronic properties. Since this remarkable discovery, much research has gone into the design, synthesis, and characterization of new chargetransfer salts. Systems are known that show not only semiconducting and metallic behavior, but also superconductivity. Most organic superconductors are based either on TMTSF (tetramethyltetrathiafulvalene)26i or BEDT-TTF [bis(ethylenedithio)tetrathiafulvalence].2«2 addition to these molecular conductors based on multi-sulfur 7r-donor molecules, salts based on multi-sulfur 7r-acceptor molecules have begim to attract an increasing interest. A unique fcimily of complexes derived from [Ni(dmit)2]~'* (where dmit = 1,3dithiole-2-thione-4,5-dithiolato) with 0 < n < 2 has recently received attention.^^' The novel electronic properties of the Ni(dmit)2 acceptor complexes are attributed to the non-bonding interactions of the acceptor entities. By using planar ligands «ind squaxe-pleinar coordinating transition metals, close packing cirrangements are formed in the crystal. With ten sulfur atoms along the periphery of the planar ligamds, S• S overlap can be large. These structtiral effects promote strong intermolecular 213

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214 interactions and suppress the Peierls distortion, leading to highly electrical conductivity. Three superconducting Ni(dniit)2 complexes have been reported. The first, TTF[Ni(dmit)2], shows high electrical conductivity at ambient presstire 300 cm~^ at 300 K to ~ 10^ cm at 4.2 K. Furthermore, under 7 kbar pressure, this compound superconducts with a Tc = 1.62 K.^^* The second salt, (Me4N)[Ni(dmit)2]2, is metallic ~ 50 cm~^ at room temperature and becomes superconducting at 5 K under 7 kbar.^^^ Finally, the ambient pressure superconductor complex a-EDTTTF[Ni(dmit)2] displays metallic-like electrical conductivity down to 1.3 K where it becomes superconducting.^^^ In order to provide further information on the nature of Ni(dmit)2 complexes, we have used electrocrystallization techniques to synthesize three Ni(dinit)2 based donor-acceptor compounds with closed-shell cations, (Ph4P)[Ni(dmit)2]3,^^''^®* (Bu4N)2[Ni(dmit)2]7-2CH3CN,269 and (Me3S)[Ni(dmit)2]2,2"'"° and measured their transport and optical properties. To our knowledge, despite the large number of interesting Ni(dmit)2 salts, relatively few optical studies have been made.'^^^'^'^"'^''^ In this paper we describe the comprehensive trcinsport and optical properties of these three organic materials. Spectroscopic methods «ire well suited to the study of such highly anisotropic crystals, providing information on both the electronic charge transfer and localized excitations at high energies as well as the vibrational features at low energies."^^' Eight infrairedactive vibrational modes in the Ni(dmit)2 stacking direction are of particular interest. Infreired cictivity of these modes can be attributed to the coupling of the totally symmetric (^4^) Ni(dmit)2 vibrational modes with the low-lying electronic charge-transfer excitation;^^® it is very sensitive to changes in the electronic structure of the crystal. Emphasis has been placed on the correlation of the spectral properties with available structural and transport data. In addition, we compare our data on (Ph4P)[Ni(dmit)2]3 to earlier results by Nakamura et a/.^^*

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215 Experimental Material synthesis The drnit"^ ligand was prepared following the procedures described by Steimecke et al?"^^ The complex (Ph4P)[Ni(dmit)2]3, was synthesized via constcint current electrocrystallization in CH3CN with 0.075 M Ph^PBr electrolyte. A current density of 1.5 /xA/cm^ was used over a period of 15 days."^^^ The complex (Bu4N)2[Ni(dmit)2]7-2CH3CN, was electrocrystallized in CH3CN with 0.1 M BU4NCIO4 electrolyte using a method similcir to that of Valade et al?^^ A current density of 1.3 nA/cm^ was used over a period of 24 days. Platelet and needle-like crystals were obtained upon harvesting. Platelets were chosen for study. The stoichiometry was confirmed by elementtd analysis.^*" The complex {Me3S)[Ni(dmit)2]2, was electrocrystallized in 1:1 acetone/CH3CN with 0.1 M Me3SBF4 electrolyte using a method similar to that of Kato et a/.^^" We used a current density of 0.5 /iA/cm^ over a period of 26 days.^^^ Material characterization Structure . All structures were solved by direct methods in SHELXTL plus^^^ from which the locations of the non-H atoms were obtained. The structures were refined in SHELXTL plus using full-matrix least squares. The non-H atoms were treated anisotropically. Crystal data is collected in Table B-1. The crystal packing array of the Ni(dmit)2 units in (Ph4P)[Ni(dmit)2]3 is unique among the Ni(dmit)2 complexes. It is shown in Figs. B-1 and B-2. The structure can be described as segregated, slightly staggered stacks of the planar Ni(dniit)2 acceptor molecules along [010], separated "side-by-side" by planes of orthogonal spacers of the Ni(dmit)2 acceptor. The acceptor stacks and spacers are separated "end-to-end" by closed-shell Ph4P+ donors also in the [010] direction.

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216 Table B-1. Structural Parameters for [Ni((iinit)2] salts. (Pli4P)[Ni(dniit)2]3 (Bu4N)2[Ni(dmit)2]7-2CH3CN'' (Me3S)[Ni(dmit)2]2 C2 P-1 X X P-1 ixArkn r^r*! i n i XI i^lXXLiV^ TVirHriir a^^A; 13 604C21 7 923d 1 b(A) 7.193(1) 22.965(3) 11.647(1) c(A) 22.960(4) 24.270(4) 17.812(2) a" 90.00(0) 108.16(1) 77.46(1) 92.60(1) 103.09(1) 85.93(1) 7" 90.00(0) 89.67(1) 81.36(1) y(A3) 2988.5(7) 7000 1585.0(3) z 2 2 2 " From ref. 269. There is an extensive amount of non-bonding orbital interactions exhibited throughout the structure. Looking within the segregated stacks of Ni(dmit)2 cicceptor units, there is no S• -S orbital overlap observed. However, there is Ni dg"^' • -S orbital overlap. As can be seen from Fig. B-2 the interplanar acceptor spacings are equidistant at ~ 3.76 A. The orthogonal spacer acceptor units have a separation of 4.058 A, which results in intermolecular interspacer S• -S distances well beyond the sum of the van der Waals radii of 3.70 A. Despite the fact that there are no interspacer or interst£ick S• -S interactions, there is a significant cimount of spacer-stack interJictions. Each Ni(dmit)2 spacer imit interacts with the six Ni(dmit)2 units within adjacent stacks. The Ni d^^ orbital of the spacers is directed toward the thiolate sulfurs of Ni(dmit)2 imits in the two neighboring molectiles. The spacing between

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217 stable and spacer is 3.426 A. A number of spacer-stack interactions are also observed involving the peripheral thiolate and thiole groups of the Ni(dmit)2 spacers. Each of these groups interact with two Ni(dniit)2 units within the adjacent stacks. The separations reinge from 3.609 A to 3.628 A; all are shorter than the vjui der Waals separation of 3.70 A. Along the [001] direction, there are no non-bonding interactions observed between the terminal thione groups of the acceptor and Ph4P''' donor units. Therefore, (Ph4P)[Ni(dmit)2]3 has a quasi-two-dimensional network of S• -S and Ni Az^• -S intermoleculax interactions. Note that our structure compcires rather well with that already reported by Nakamura et al?^^ except that we have chosen the c-axis as half of theirs due to difficulties with data collection, and subsequent data resolution, on a unit cell where one axis is more than 45 A in length. The structure was solved and refined in the C2 space group and showed no signs of disorder. The final refinement yielded R and wR values of 4.55 and 4.61, respectively for I and 3.29 and 3.96 for II. Several groups have reported different stoichiometries for (Bu4N)2[Ni(dmit)2]7-CH3CN. According to Valade et a/.,^^^ this complex has the stoichiometry (Bu4N)2[Ni(dniit)2]72CH3CN based on X-ray and elemental analysis. The structure can be described as consisting of thick layers of Ni(dmit)2 entities oriented parallel to (001) and separated by sheets of BU4N+ cations and CH3CN molecules. Within a layer the Ni(dmit)2 species are arreinged in stacks along the [110] direction. A stack consists of quasiparallel quasi-planar Ni(dmit)2 units arranged in alternating centrosynunetric triads and tetrads. The axes of the triads and tetrads are parallel but make an angle of about 21° with the overall stacking direction [110]. Given the tt interactions along the stacks on the one hand and the interstack S• -S interactions on the other, it is clear that the structure arrangement of (Bu4N)2[Ni(dmit)2]7 • 2CH3CN cannot be viewed as a classical one-dimensional system but is much more nearly two-dimensional.

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218 The structure of (Me3S)[Ni(
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219 Optical spectroscopy . Near-normal polarized reflectance measurements were mzwie on single-crystal samples. Far-infrared cind midinfrared measurements were ccirried out on an Bruker 113v Fourier-trainsform infrared spectrometer using a 4.2-K bolometer detector (30-600 cm~^) and a B-doped Si photoconductor (450-4000 cm~^). Wire grid polarizers on polyethylene and AgBr were used in the far and midinfraired, respectively. A Perkin-Elmer 16U grating spectrometer in conjimction with both thermocouple, PbS, aind Si detectors was used to measure the spectra in the infrared to the ultraviolet (1000-32000 cm~^), using wire grid and dichroic polarizers. Experiments were performed with light polarized parcdlel and perpendicular to the Ni(dmit)2 stacking axis. The reflectance was calibrated with a reference cJuminum mirror. In order to correct for size differences between sample and reference and to compensate for scattering losses, all samples were coated with a thin aluminum layer iifter the optical measurements were finished. The final corrected reflectance was obtained by rationing the initial reflectance (no coating) to the reflectance of the coated sample, then multiplying the ratio by the alumintmi reflectance. After the reflectance spectra were measured, the optical properties were determined by Kramers-Kronig analysis.^*^ Because an extremely large frequency region was covered, Kramers-Kronig analysis should provide reasonably accurate values for the optical constants. To perform these transformations one needs to extrapolate the reflectance at both low and high frequencies. At very low frequencies the reflectance was assumed constant. Between the highest-frequency data point and 10* cm~^ the reflectance was assumed to follow a power law of u)~^; beyond this frequency range a free-electron-like behavior of a>~'* were used.

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220 Results Transport properties Temperature-dependent four-probe electrical conductivity measurements are shown in Fig. B-4. Semiconducting behavior is found for all of the compounds investigated. The conductivity decreases from its 300 K value when temperature is decrejised. The typical temperature dependence of the conductivity may be expressed eis: where Eg is the semiconductor gap. The values of room-temperature conductivity and the thermal activation energy Ea = Eg/ 2 are listed in Table B2 263,268,269,283-285 j,^^ results for our materials cire compared to those observed previously for [Ni(dmit)2] salts with different closed shell organic cations. For (Ph4P)[Ni(dmit)2]3 our roomtemperature conductivity agrees with that published by Nakamura et al}^^ However, the thermal activation energy measured in this work is smaller thcin foimd by Nakamura et a/.^^* In contrast, our conductivity parameters for (Bu4N)2[Ni(dmit)2]7 • 2CH3CN coincide with prior Valade et al^^^ data. Interestingly, both (Ph4P)[Ni(dmit)2]3 and (Bu4N)2[Ni(dmit)2]7 • 2CH3CN have high conductivities and low activation energies. This suggests the presence of fractional oxidation states. An additional result is that there is a change in the apparent activation energy aroimd 100 K in (Ph4P)[Ni(dmit)2]3. The plot of log a vs. 1/T does not obey a single Unear relationship; instead two different slopes were obtained above and below a crossover point of 100 K. Ea is smaller at low temperature, probably due to impurity effects. Another formula for the conductivity comes from the model proposed by Epstein and Conwell:^*^''^^^ (B-1)
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221 where fi{T) ~ fioT'" and n oc . The conductivity is a product of a strongly temperat liredependent mobility and an activated carrier concentration. A fit of this model to our experimental results is imsatisfactory. Table B-2. Conductivity parameters for [Ni(dmit)2] salts with closed shell cations. Compound (^RT ^ cm ^ ) T Ea (meV) Ref. (Ph4P)[Ni(dmit)2]3 7 < lOOK 10 This work > lOOK 17 10 < 125K 35 268 > 125K 46 (Bu4N)2[Ni(dmit)2]7-2CH3CN 1 42 This work 1~10 100-20 269 (Me3S)[Ni(dmit)2]2 6.5x10-2 130 This work (Ph4As)[Ni(dmit)2]4 10~15 < 160K 10 283 > 160K 30 (tmiz)[Ni{dmit)2]" 0.21 110 284 (Et4N)[Ni(dmit)2] 4x10-5 250 285 (Et4N)[Ni(dmit)2]2 4.5x10-2 263 (Me4N)[Ni(dmit)2] 5x10-^ 320 285 (Pr4N)[Ni(dmit)2] 430 285 (Bu4N)[Ni(dmit)2] 3x10-* 510 285 " tmiz = 1,2,3-trimethyhmidazohum

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222 Optical results Polarized reflectance . Figure B-5 shows the polarized room-temperature reflectance from the (001) face of (Ph4P)[Ni(dmit)2]3 and (Bu4N)2[Ni(dmit)2]7-2CH3CN and the (010) face of (Me3S)[Ni(dmit)2]2 over the entire spectral range. Data «ire shown for polarizations parallel and perpendicular to the Ni(dmit)2 stacking axis. For the electric field polarized parallel to the stacking direction, a common feature of the three compoimds is a value of 40% to 60% in the farto midinfrared with a drop to values of a few percent around 3000 to 4500 cm~^. Superimposed on this reflectaaice is a series of narrow peaks of varying amplitudes at frequencies typical of molecular vibrations. For higher frequencies, the spectra is cdmost dispersionless, showing only several weak electronic features. In the case of (Ph4P)[Ni(dmit)2]3, such data have been reported over the limited frequency reinge of 600 to 25000 cm~^ by Nakamura et al?^^ The reflectance values we measured in the region below 1000 cm~^ axe up to 20% higher than that of Nakamura et al.^^^ However, the minimum drop of the reflectance aroimd 3000 cm~^ coincides with those previous data. The reflecteince when the polarization is perpendicular to the Ni(dmit)2 stacking axis is also shown in Fig. B-5. There is a marked contrast for polarization of the light parallel cind perpendicular to the Ni(dmit)2 stacking cixis. The reflectivity is low (~ 15%), flat, and almost featureless for (Bu4N)2[Ni(dmit)2]7-2CH3CN and (Me3S)[Ni(dmit)2]2. In contrast, the (Ph4P)[Ni(dmit)2]3 perpendicular spectra is similar in shape to that with parallel poltirization up to 1000 cm~\ but differs in the deep minimum of the reflectance and in the higher frequency region. Optical conductivity . The Kramers-Kronig transformation of the stacking-cixis reflectance data of Fig. B-5 yields the real part of the conductivity (Ji{io) shown in Fig. B-6. The spectra display a broad low-energy bcind, which contains a majority of the oscillator strength and several vreak electronic structures at higher frequencies.

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223 In all cases they show a conductivity maximum at finite frequency in contrast to the simple Drude behavior of an ordinary metal, which is mfiximum at u; = 0 and then decreases monotonically with increasing frequency. The conductivity mziximum shifts to higher frequencies cis the dc conductivity decreases. This behavior is in itself suggestive of an optical gap and possibly a trcinsport gap of increasing magnitude. Previous work on (Ph4P)[Ni(dmit)2]3 by Nakamura et a/.^^* found the value of the conductivity at the maximimi to be ~ 140 cm~\ about three times smaller than our value of ~ 520 f2~^ cm"^ This difference is consistent with the fact that the reflectance level we observed in the infrared region is higher than that of Nakamura et al}^^ At low frequency, the spectra exhibit many shcirp vibrational features. Several of these modes are Ag vibrations of the Ni(dmit)2 molecule, activated by coupling to the low-energy electronic beind.^^* Note that accompanying the shift to higher frequencies of the conductivity maximum, there is an increase of the amplitude of the midinfrared vibrational structures from this electron-molecularvibration (EMV) coupling. The appearance of these features also changes depending on their frequency location relative to the conductivity maximum. When their frequencies are well below that of the broad maximum they appe«ir as ordinary (Lorentziein) resonances whereas when their frequencies overlap the electronic continuima, they have Fano^** line shapes: an antiresonance or dip preceded by a peak on the low frequency side. Extrapolating the frequencydependent conductivity to zero frequency, we obtain an estimate of the dc conductivity on the order of (Me3S)[Ni(dmit)2]2 (< 1 cm-i) < (Bu4N)2[Ni(dmit)2]7-2CH3CN (1 ~ 5 fi-icm"^) < (Ph4P)[Ni(dmit)2]3 (5 ~ 15 fi-i cm ) at 300 K. These values are in reasonable agreement with those obtained by four-probe dc measurements (Table B-2). (We note that that the of KramersKronig analysis is not to sensitive to conductivities below about 0.1 fi~^ cm~^ on

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224 account of limits in the accuracy of the reflectance measurements.) An estimate of the semiconducting energy gap is also obtained from the low-energy electronic band shown in Fig. B-6. The frequency where the conductivity has risen to half its maximum value yields an estimate of gap values Egi (Ph4P)[Ni(dmit)2]3 (~ 270 cm~^ = 34 meV) < (Bu4N)2[Ni(dmit)2]7-2CH3CN (~ 650 cm"! = 81 meV) < (Me3S)[Ni(dmit)2]2 (~ 1750 cm~^ = 220 meV). These are consistent with transport measurements discussed above which give Eg-. (Ph4P)[Ni(dmit)2]3 (~ 34 meV) < (Bu4N)2[Ni(dmit)2]7-2CH3CN (~ 84 meV) < (Me3S)[Ni(dmit)2]2 (~ 260 meV). As expected, the ro), and optical {u)io), frequency of each mode. The dielectric function of (Ph4P)[Ni(dmit)2]3 is negative in the far infrared (characteristic of free carriers), cind has a zero crossing eiroimd 110 cm~^ The transition across the energy gap is suflSciently strong to give negative values between 300 and 800 cm~^. By extrapolating the low frequency fcir-infrcired data to zero frequency, we estimate the

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225 static dielectric constant for (Bu4N)2[Ni() + ie2{u;)] using a simi of Lorentz oscillators:"^^"^ = E 2 + ^oc, (B-3) where Upj, uj, and 'yj are the oscillator strength, center frequency, cind scattering rate of the j^^ transition and Cqo represents the other higher frequency contributions to the dielectric function. The parameters obtained for our samples axe listed in Table B-3. The results for the fit are compared to ei(a;) in Fig. B-7. Oscillator strength simi rule . Considerable information about the electronic structure of Ni(dmit)2 salts can be extracted from the oscillator strength simi rule.^*^ The effective nimiber of electrons participating in optical transitions for energies less than ?iuj is given by m. ""^-^ = ^ /.'.(u.^', (B-4) 0 where m* is the effective mass of the carriers and Nc is the number of Ni(dmit)2 molecules per unit volimie. Plots of N^g are shown in Fig. B-8. In the stacking direction, {^)Ncf[ at first rises rapidly in the low-frequency region, begins to level off in the near-infrared, and then rises again above the onset of the high-frequency electronic bands. From the plateau values of the integrated oscillation strengths in the near-infrared, assuming N^ff of (Ph4P)[Ni(dmit)2]3,

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226 Table B-3. Parameters of Lorentz fit to the stacking-axis reflectance of [Ni(dmit)2] salts. O n a f nr<3 PJ (cm-^) J (cm-i) 7i (cm-i) P Vi J P f Ni Mmit "1 o 1 ^ 1 1380 292 60 2 1765 447 281 3 2517 1000 1356 4 1936 1700 982 5 2100 5000 2000 6 2050 7800 2000 7 2500 11500 3000 8 1100 15000 800 €00 = 1-1 (Bu4N)2[Ni(dmit)2]7-2CH3CN 1 4900 1050 990 2 2200 4700 1331 3 2286 7300 2023 4 3500 10000 4500 5 1400 11700 2000 = 1 19 (Me3S)[Ni(dmit)2]2 1 4650 2225 1087 2 2954 3413 1431 3 2900 5560 1355 4 4019 8025 2269 5 5250 11250 3938 6 1750 14000 1000 = 1.19

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227 (Bu4N)2[Ni(dinit)2]7-2CH3CN, and (Me3S)[Ni(clmit)2]2 to be 0.33, 0.29, and 0.5, we estimate m* = 4.17 mg, m* = 2.86 mg, and m* = 4.0 me respectively. As seen in Fig. B-8, below 800 cm~^ the stronger oscillator strength of (Ph4P)[Ni(dmit)2]3 due to smaller optical gap is readily evident. In contrast, the enhanced contribution of the mid-infrared electronic band is seen in (Bu4N)2[Ni(dmit)2]7-2CH3CN. The two curves of (Ph4P)[Ni(dmit)2]3 and (Bu4N)2[Ni(dmit)2]7-2CH3CN come together nicely around 20000 cm~^. In the polarization perpendiculcir to the stacking axis, (^)iVeff is small in the infrared but rises rapidly at higher frequencies. Discussion Electronic features In principle, the electronic transitions which appear in the (T-[{(jj) spectra of these Ni(dmit)2 organic solids will fcill into two classes. On the one hand, those at high frequencies generally cire the result of localized-excitation bands in the molecule. On the other hand, transitions at lower frequencies that are along the stacking direction will correspond to charge-transfer excitations between the Ni(dniit)2 molecules. The frequencies and oscillator strengths of these chargetransfer bands axe clearly related to the electronic structure of the compound, but their interpretation is determined by three types of interactions cimong the unpaired electrons occupying the highest molecular orbited in the solid. These interactions are the overlap of the electronic wave functions between sites, the Coulomb repulsion of two electrons on the Scime or adjacent sites, and interactions of the electron with phonons (both lattice vibrations and intreimolecular modes of the molecule). Theoretical models for the electronic structure of these materials have emphasized the importance of one or the other of the above interactions, e.g., tight-binding theory,^*^ Hubbard model,2^° and Peierls model.^^^

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228 The simple 1:1 ratio of donoracceptor Ni(dmit)2 salts such as (Me4N)[Ni(dmit)2], (Et4N)[Ni(dmit)2], (Pr4N)[Ni(dmit)2], and (Bu4N)[Ni(dinit)2], have one unpaired electron on each Ni(dinit)2 molecule. Because of the laxge on-site Coulomb repulsion (Hubbard U), these materieds display very low dc electrical conductivity at room temperature (Table B-2). Their electronic structure consists of either completely filled or completely empty bands. Hence, they are often referred to as "Mott-Hubbard" insulators. For the complex salts, the most common stoichiometric ratio is 1:2 corresponding to the quaxter-filled-band case such as (Me3S)[Ni(dmit)2]2, with electrons on average occupying every other site. In this case, it is important to consider an extended Hubbard pictiire.'^^"'"^^^"'^^'* which includes hopping from site to site (f), on-site Coulomb repulsion energies (U), nearest-neighbor energy (Vi), and the nextnearestneighbor energies (V2). Finally, the behavior of other complex salts, such as (Ph4P)[Ni(dmit)2]3(l:3) or (Bu4N)2[Ni(dmit)2]7-2CH3CN (2:7), is much more complicated than the 1:1 or 1:2 cases. Let us look first at the simple 1:1 or 1:2 donor-acceptor Ni(dmit)2 salts. An early optical study of (Bu4N)[Ni(dmit)2], made by Papavassiliou et al,^^^ shows a low-frequency band at 8850 cm~^ The solution spectra of [Ni(dmit)2]^~ and [Ni(dmit)2]~, reported by Tajima et al.,^^^ have the lowest intramolecular optical excitation at 8700 cm~^ Due to the symmetry of the molecular orbitals, this transition should be polarized along [Ni(dmit)2]'s molecular long iixis. Additional work on the polarized reflectance of 0MTSF-[Ni(dmit)2] (OMTSF: bistetramethyleneTSF) has been reported by Jacobsen et al.^^^ An interpretation of the spectra is that the chcirge transfer excitation is observed at 2600 cm~^ and the transitions at 10000-12000 cm~^, at 17000 cm~^, and above may be associated with intramolecular excitons. In contr«ist, the temperature-dependent polairized reflectance on a-EDT-TTF[Ni(dmit)2], (Me4N)[Ni(dmit)2]2, (Me2Et2N)[Ni(dmit)2]2, and a-

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229 (Et2Me2N)[Ni(diiiit)2]2, was studied by Tajima et al.^''^ and Tamura et al.^"^^ In all cases, the measured spectra exhibit a Drude-like shape down to 20 K. With the above information in mind, let us turn our attention to the frequencydependent conductivity, cri{uj), of the three Ni(dmit)2 compounds shown in Fig. B-5 and the fit peirjimeters in Table B-3. For the typical quarter-filled-band case, such as (Me3S)[Ni(dmit)2]2, the mid-infrared spectral features in the Ni(dmit)2 stacking direction consist of two strong, broad absorptions. We interpret these bands to be electronic charge transfer between Ni(dmit)2 molecules within the stack. The electronic absorption band at ~ 2000 cm~^ corresponds to the charge transfer: Ni(dmit)2'' + Ni(dmit)2" — > Ni(dmit)2~ + Ni(dmit)2°. The breadth of this band in (Me3S)[Ni(dmit)2]2 may result from the overlap of two intratetramer charge-transfer excitations as well as one intertetramer charge-transfer excitation. The energy for this excitation depends on V[ and hopping integrals, but not on U. The bands at ~ 5560 and 8000 cm~^ are attributed to the charge transfer process: Ni(dniit)2~ -INi(dmit)2~ — > Ni(dmit)2*' -fNi(dmit)2^~. These bands are governed by the Hubbard parameters for on-site (U) and nearest neighbor (Vi) Coulomb repulsions. Again, the presence of two bands may come from intratetramer and intertetramer charge-transfer excitations. For the electric field polarized perpendiculeir to the stacking axis, three absorption bands at ~ 11250, 13000, and 18000 cm~^ are thought to be intramolecular localized excitations or molecular excitons. Note that the energy of the lowest localizedexcitation is 11250 cm~^ rather than 8700 cm~^ observed in Ni(dmit)2 solution spectra.2^2 This blue shift (by ~ 0.3 eV or 2500 cm"^) is the usual Davydov shift^^'S.ase which is expected due to the interaction between the transition dipole moments on adjacent molecules in the dimer. The first two localized excitations cire also seen in the parallel polarization on account of the triclinic space group. The fact that in

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230 these Ni(dmit)2 sailts the moleculax plane is not perpendicular to the stacking axis gives rise to a strong coupling and mixing among these intramoleculeir excitations for two different polarizations. Despite the significantly different stoichiometric ratios of donor-acceptors, the ai{u) spectra of (Me3S)[Ni(dmit)2]2, (Bu4N)2[Ni(dmit)2]7-2CH3CN, and (Ph4P)[Ni(dmit)2]3 are similar in character and typical of semiconducting chargetransfer salts. In the case of (Bu4N)2[Ni(dmit)2]7-2CH3CN, the stacking direction has a transition at ~ 1050 cm~\ attributed as above to charge transfer from a Ni(dmit)2 radical anion to a neutral molecvde within a Ni(dmit)2 triad or tetrad. The higherfrequency peaks, at ~ 4000 and 7300 cm~\ are attributed to charge transfer between two radical Ni(dmit)2 anions. The spectrum perpendicular to the stacking axis shows transitions at ~ 10000, 11400, and 18700 cm~^ which are due to the localizedexcitation of the isolated Ni(dmit)2 anion. Again, some of these absorption bands are adso observed along the stacking cixis. Finally, in the case of (Pli4P)[Ni(dmit)2]3, there are two low-energy electronic excitations (at ~ 300-450 cind 1000-1700 cm~^) for the electric field polarized cJong the Ni(dmit)2 stacking axis. The structure of this material is imique: two of the three Ni(dmit)2 anions form stacking colunms whereas the remaining Ni(dmit)2 anion fills the spa<;es between the columns. The optical data can be correlated with this structuTjJ information. We attribute the 300-450 cm~^ peak to charge transfer excitations within Ni(dmit)2 stacking colxmans. The higher peak, at ~ 1000-1700 cm~^, is attributed to a charge transfer to an adjacent neutral molecule. Interestingly, the spectrum perpendicular to the stacking axis displays low-lying peaks at similar energies, but hcis considerably smaller oscillator strength. The bands occurring at ~ 5000 and 7800 cm~\ are attributed to a chargetransfer excitation between Ni(dmit)2 ions. The transitions of an electron excited to a higher orbited or localized excitation

PAGE 239

231 axe seen to be polcirized along both pax«illel and perpendicular to stacking axis at frequencies of ~ 11500 and 15000 cm~^ Although these three Ni(dmit)2 compounds have different chemicaJ modifications of the donor cation, an interesting correlation can be made between spectral properties and available structural information. As discussed above, (Ph4P)[Ni(dmit)2]3 and (Bu4N)2[Ni(dmit)2]7-2CH3CN have a nearly two-dimensional structure as opposed to the rather quasi-three-dimensional network in (Me3S)[Ni(dmit)2]2The obvious question now is why does the increased dimensionality of (Me3S)[Ni(dmit)2]2 result in a lower electrical conductivity, a higher activation energy for conduction, and a larger Vtdue of optical gap than the other two Ni(dmit)2 salts? In principle, the nature of the donor is primarily responsible for the different manner of stacking in these Ni(dmit)2 materials. It particularly influences the mode of overlap between Ni(dmit)2 molecules. Smzdl cations such as Me3S"'' promote close-packing arrangements, but «dso give room for dimerization. Larger ones encourage uniform spacing but adso tend to give imusual stoichiometries or packing arrangements. There are always counterexamples; for example, there is a Ni{dmit)2 system with a small cation, (Me4N)[Ni(dmit)2]2,^*^ that displays metallic electronic properties and becomes superconducting under pressure. In any event, it is clear that the situation is quite complex and that any serious attempt to tmderstand the electronic structure of these Ni(dmit)2 salts needs a careful consideration of the role of both donor and acceptor in the electronic band structure.2^'^'2^* Vibrational features Vibrationctl mode tissignments . We will now turn to a discussion of the vibrational features. In general, the vibrational modes Ccin be divide into two classes. Those involving motion within the Ni(dmit)2 einion itself are classified as intra-molecular in nature, whereas the modes involving collective motion of the Ni(dmit)2
PAGE 240

232 cation stacks are inter-moleculax or lattice modes. The intra-moleciilar modes occur at high frequencies, and include the totally symmetric phonon modes
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233 Table B-4. Frequency and assignment of vibrational features in (a) infrared and (b) Raman spectra of [Ni(dmit)2]~". n = 2" n = 2* n = 1" n = 0.25'= n = 0" Assignment (a) infrared 1440 s 1430 s 1353 s 1260 1260 s (C=C) 1065 s 1035 1063 s 1055 1088 m (C=S) 1034 s 1015 1030 m 1064 s (C=S) 917 m 900 m 902 m 890 m (C-S) 885 m 880 sh (C-S) 472 m 455 vam 498 m 495,490 485 m (Ni-S) 311 m 310 m 317 s 328 m (Ni-S) n = 2"^ n = 0.25'= Assignment (b) Raman 2329 1445 1332 1075 1060 1061 520 494 360 364 320 344 132 (C=C stretching) (ring deformation) (Ni-S stretching) » FVom ref. 278, * Prom ref. 281, ^ Prom ref. 271, Prom ref. 275. s: strong, m: mediimi, sh: shoulder.

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234 teractions with the electronic conductivity. In particular, as the princip«J maximum of the conductivity overlaps with the vibrational frequencies, these EMV effects become increasingly pronounced. In the case of our Ni(dmit)2 compounds, many of these Ag modes are seen as antiresonances whose minima correspond to the vibrational features. Thus, in the presence of the electron-moleculcU' vibration coupling, the normally infrared-inactive totally-syrametric Ag intramoleculaj vibrational modes become infrared active for electric fields polcirized in the direction of the Ni(dmit)2 stacking axis. The highest-frequency EMV vibrational feature is in the 1300 cm~^ range. We have assigned this feature to the C=C stretching Ag mode. It clearly has the effect of producing a broad minimum in crj(a;) for (Ph4P)[Ni(dmit)2]3 and a deep and strong minimimi for (Bu4N)2[Ni(dn:iit)2]7-2CH3CN. For the spectrtmi of (Me3S)[Ni(dmit)2]2 there appears to be a a typical Lorentzian-shaped peak. However, the intensity of this peak is far too strong to be an ordinciry vibrational peak, and in fact the polarization is also wrong, so we attribute it also to an EMV feature. The lineshape is as it is because the main electronic band is at higher frequencies in this compound. The btind near 1070 cm~^ is due to EMV coupling of the Ag mode involving C=S stretching. The modes near 940 cm~^ are believed to be C-S stretching Ag bands. The remaining features form a group from 100 to 550 cm~^. The bcinds which are of unambiguous origin are the ring deformation Ag mode near 514 cm~\ the Ni-S stretching Ag mode near 350 cm~^ and 320 cm~\ and one Ag mode near 139 cm~^. Apart from the strong features mentioned above, we observe an interesting cintiresonance at 514 cm~^ for polarization perpendicular to the stacking axis in (Ph4P)[Ni(dmit)2]3. We believe that this unusual feature is due to to ring deformation of the tetraphenylphosphonium cation. Ordinary infrared-active modes involving C=C at ~ 1430 cm~^ and C=S at ~ 1100 cm~^ are resolved only in

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235 (Ph4P)[Ni(dmit)2]3Other infrared active modes should correspond to Ni-S vibrations near 480 and 330 cm~^ for three compounds. Additional vibrational structures are seen at ~ 723, 730, 746 cm~^ in (Ph4P)[Ni(dmit)2]3 and at ~ 341, 400 cm"^ in (Me3S)[Ni(dmit)2]2 for different polarizations. These features might be due to Ni(dmit)2 modes of other symmetry as well as those of donor cations. Dimer model . We analyze our results for Ni(dmit)2 materials in term of a model by Rice et al?^^ based on isolated dimers. We have fitted this model to the conductivity spectrum of the most insulating of our salts, (Me3S)[Ni(dmit)2]2. In this theory, the frequency dependent conductivity is where a is the dimer separation, N is the number of dimers per unit cell, and H is the volume of the unit cell. The quantity D{ (B-6) with A„ the dimensionless electronphonon coupling constant, u>n the unperturbed frequency, and 7„ the phonon linewidth for the nth Ag mode. X(a;) is the reduced electronic polarizability, XM = , ^''^V , (B-7) where is frequency and 7e is the linewidth of the electronic charge transfer excitation. The dimensionless coupling constants are written as where X(0) is the zero frequency limit of Eq. B-7. It is the g„ which are the fundamental microscopic electron-molecular-vibration coupling constants.

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236 Table B-5. Observed vibrational frequencies in [Ni((iniit)2] salts. (Pb4P) (Bu4N) (MeaS) Preq. Inten. Pola. Freq. Inten. Pola. Preq. Intes. Pola. A Ag 1342* m Ell II 1340*, 1288* vs E|| 1333,1207 m,vs E|| 1063* w Gii II 1069* vs 1072,1042 m E|| 941* vw Ell 953* ,939* s E,| 935,916 m,s E|| 514* w M Ell II 514* w E|| 508 w E„ 345* w Ell II 345* w E|| 356 w E|| 319* vw Ell II 319* m E|| 321 s E„ 139* w Ell 139* w E|| 131 w E|| 1981* vw Ell II 1974*,1974 vw Ell, Ex II 1960* vw E|| 1570* vw Ell II 1572* vw Ell II 1580* vw E|| 1431,1425* vw E±,E|| ' II 1429* vw E|| 1107,1097* vw Ei,E|| ' II 822* vw II 835* vw Eji 841 sh E|| 783 vw E± 783*, 781 vw E|| ,Ei 781 vw Ex 696*, 686 vw Ell, El II ' 696 vw E|| 696 vw E|| 673* vw Ell II 675* vw Ell II 654* vw E|| II 650* vw Ell II 638 vw E|| 532*, 532 vw Ell, El II ' 538* vw Ell II 528 vw E|| 497, 493* vw Ej.,E|| 490* vw E|| 477*, 475 vw E||,Ej. 479* vw E|, 480 vw E|| 440*, 439 vw E||,Ej. 433* vw E|| 433 vw E|| 298*, 295 vw E||,Ei 298*, 295 vw E||,Ej. 294 vw Ex 286, 283* vw Ej.,E|| 284* vw E|| 279 vw E|| 193*, 187 w,vw E||,Ej. 192 vw Ex 109* m E|| vs: very strong, s: strong, m: medium, w: weak, vw: very weak, sh: shoulder, *antiresonance.

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237 A fit of this model to the (Me3S)[Ni(dmit)2]2 data is shown in Fig. B-10. The structural parcuneters used in the calculation were the separation between the Ni(dimt)2 molecules a = 3.49 A and the unit-cell volume il = 1585 A^. The fitted pcirameters for the chairge-trcinsfer band are a trcinsfer integral of t = 1200 cm~^ The charge-transfer energy and electronic linewidth are Ud = 2180 cm~^ an 7e = 1400 cm~^. The experimental v«Jues for the unperturbed phonon frequencies u;„, EMV coupling constamts ^Tn, and dimensionless electron-phonon coupling constants A„ are listed in Table B-6. Table B-6. Electron-molecular-vibration coupling parameters for (Me3S)[Ni(dmit)2]2. (cm-') gn (cm-i) A„ 1296 330 0.0934 1053 100 0.0106 930 110 0.0145 512 70 0.0106 359 85 0.0224 335 130 0.0561 137 90 0.0660 Total 0.2736 "Obtained from plot of Re[l/
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238 lated dimer in a 4ifc/ configuration with one electron on two sites. Instead, the interdimer interactions aie strong and the Ni(dmit)2 stack is composed of relatively isolated tetramers. The model of electron-molecular vibrational coupling extended by Yartsev-^^^ to describe isolated tetramers might provide a better agreement with our experimental spectrum. Summary In stmamary, we have made extensive measurements of the optical and transport properties of (Ph4P)[Ni(dmit)2]3, (Bu4N)2[Ni(dmit)2]7-2CH3CN, and (Me3S)[Ni(dmit)2]2 compotmds. The optical properties are dominated by vibrational features at low frequencies and by electronic excitations at higher frequencies. The observed vibrational features include ordinary intramolecular modes and seven "anomalous" infraredactive vibrational modes. The latter absorption results from the interaction of these vibrations with the unpaired electron on the Ni(dmit)2 anion. A series of electronic excitations axe observed for the electric field polarized along the Ni(dmit)2 stacks. The low-lying peaks are attributed to a charge transfer from one Ni(dmit)2 anion to an adjacent neutral molecule, whereas the excitations higher in frequency axe attributed to a chcirge transfer between two radiccil Ni(dmit)2 «inions. We have excimined the vibrationtJ modes in these three materials. From cinalysis of the Ag modes, values for the electron-phonon coupling constants in (Me3S)[Ni(dmit)2]2 were obtedned. We have also attempted to clarify some of the confusion which exists in the literature by systematically 2issigning vibrational modes of Ni(dmit)2 molecules in the optical spectra.

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239 Fig. B-1 View down the b axis of (Ph4P)[Ni(dmit)2]3. The dotted Unes resent S• -S and Ni• -S distances that are less than the sum of the der Wcials radii.

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240 Fig. B-2 View down the c axis of (Ph4P)[Ni(dmit)2]3 showing the array of stacks and orthogonal spacer Ni(dmit)2 units. (Ph4P+ cations have been removed for clarity) Dotted lines represent non-bonding interactions.

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241

PAGE 250

242 Fig. B-4 The dc conductivity normalized by the room-temperature value of (Ph4P)[Ni(dmit)2]3, (Bu4N)2[Ni(dmit)2]7-CH3CN, and (Me3S)[Ni(dmit)2]2 vs. temperature.

PAGE 251

243 Photon Energy (eV) 0.1 1 1 .0 0.5 0.0 0) o c D "o 0.5 _^ s—
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Photon Energy (eV) Fig. B-6 Frequency-dependent conductivity obtained by KramersKronig analysis of the room temperature reflectance of (a) (Ph4P)[Ni(dmit)2]3, (b) (Bu4N)2[Ni(dmit)2]7-2CH3CN, and (c) (Me3S)[Ni(dmit)2]2. The conductivity is shown paraUel and perpendicular to the stacking axis.

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245 Photon Energy (eV) 0.1 1 CO Frequency (cnn ) Fig. B-7 The real part of the dielectric function (dash-dotted Une) obtained by Kramers-Kronig analysis of the room temperature reflectance of (a) (Ph4P)[Ni(dinit)2]3, (b) (Bu4N)2[Ni(dmit)2]7-2CH3CN, and (c) (Me3S)[Ni(dmit)2]2 along the stacking axis. Lorentz fit to the reflectance data is shown as the solid lines.

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246 Photon Energy (eV) 0.0 0.50 0.2 0.4 0.6 0.8 1.0 1.2 0.25 0.00 ^ 0.25 E 0.00 0.25 0.00 (a) E Parallel E Perpendicualr 0 (b) (c) E Parallel E Perpendicular E Parallel E Perpendicular 2000 4000 6000 8000 10000 -1 Frequency (cm ) Fig. B-8 The sum rule for (a) (Ph4P)[Ni(dmit)2]3, (b) {Bu4N)2[Ni((iinit)2]7-2CH3CN, and (c) (Me3S)[Ni(dinit)2]2 for polarization paraUel and perpendicular to the stacking direction.

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247 0.00 600 300 ^ 0 T E o G 300 0 300 0 0 Photon Energy (eV) 0.05 0.10 0.1 5 0.20 ' ' '(a)' ' E Parallel E Perpendlcualr J'*^— .VS-M.-^' ' 'f^—^:-^ . ^ — 7 — d ^ E Parallel E Perpendicular E Parallel /\ E Perpendicular 500 1000 1500 Frequency (cm~^) 2000 Fig. B-9 Expanded portions of the conductivity spectra of (a) (Ph4P)[Ni(dmit)2]3, (b) (Bu4N)2[Ni(dmit)2]7-2CH3CN, and (c) (Me3S)[Ni(dmit)2]2 in the range 0-2000 cm~^

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248 0.0 500 400 T S 300 200 1 00 Photon Energy (eV) 0.1 0 0.2 0.3 (Me3S)[Ni(dmit)2]2 Experiment Theory 1 000 2000 -1 Frequency (cnn ) 3000 Fig. B-10 Isolated dimer fit (solid line) to the frequency-dependent conductivity (dash-dotted line) of (Me3S)[Ni(dmit)2]2.

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REFERENCES 1. J.G. Bednorz and K.A. MuUer, Z. Phys. B 64, 189 (1986). 2. T. Timusk and D.B. Tanner in Physical Properties of High Temperature Superconductors I, edited by D.M. Ginsberg (World Scientific, Singapore, 1989) p. 339. 3. G.A. Thomcis, in Proceeding of the Thirty-Ninth Scottish Universities Summer School in Physics of High Temperature Superconductivity, D.P. Tiinstall ajid W. Bairford, editors, (Adam Hilger, Bristol, Philaidelphia and New York, 1991) p. 169. 4. D.B. Tanner and T. Timusk, in Physical Properties of High Temperature Superconductors III, edited by D.M. Ginsberg (World Scientific Press, 1992) p.363. 5. M.W. CofFey and J.R. Clem, Phys. Rev. B 46, 11757 (1992). 6. M.W. Coffey and J.R. Clem, Phys. Rev. B 48, 342 (1993). 7. C.J. van der Beek, V.B. Gesgjenbein, and V.M. Vinokur, Phys. Rev. B 48, 3393 (1993). 8. W.F. Vinen, in Superconductivity, edited by R.D. Pcirks (Marcel Dekker Inc., New York, NY 1969). 9. J. Owiiaei, S. Sridhar, and J. Talvacchio, Phys. Rev. Lett. 69, 3366 (1992). 10. P.P. Nguyen, D.E. Gates, G. Dresselhaus, and M.S. Dresselliaus, Phys. Rev. B 48, 6400 (1993). 11. M. Golosovsky, M. Tsindlekht, H. Chayet, and D. Davidov, Phys. Rev. B 50, 470 (1994). 12. S. Revenaz, D.E. Gates, D. Labbe-Lavigne, G. Dresselhaus, and M.S. Dresselhaus, Phys. Rev. B 50, 1178 (1994). 13. B. Parks, S.Spielman, J. Orenstein, D.T. Nemeth, F. Ludwig, J. Clarke, P. Merchant, and D.J. Lew, Phys. Rev. Lett. 74, 3265 (1995). 14. R.P. Mallozzi, J. Orenstein, J.N. Eckstein, and I. Bozovic, (to appear in Phys. Rev. B) (1997). 249

PAGE 258

250 15. J. Orenstein, R.P. Mallozzi, and B. Paxks, (to appear in Superconductors in a Magnetic Field, edited by Carlos Sa de Melo) (1997). 16. L.C. Briinel, S.G. Louie, G. Martinez, S. Labdi, and H. Raflfy, Phys. Rev. Lett. 66, 1346 (1991). 17. K. Karrai, E.-J. Choi, F. Dunmore, S. Liu, H.D. Drew, Qi Li, D.B. Fenner, Y.D. Zhu, and F.-C. Zhang, Phys. Rev. Lett. 69, 152 (1992). 18. K. Karrai, E.-J. Choi, F. Dunmore, S. Liu, X. Ying, Qi. Li, T. Venkatesan, and H.D. Drew, Phys. Rev. Lett. 69, 355 (1992). 19. T.C.Hsu, Phys. Rev. B 46, 3680 (1992). 20. T.C. Hsu, Physica C 213, 305 (1993). 21. E.-J. Choi, H.-T.S. Lihn, and H.D. Drew, Phys. Rev. B 49, 13271 (1994). 22. H.D. Drew, E.-J. Choi, and K. Karrai, Physica B 197, 624 (1994). 23. Y. Shimamoto, T. Takamasu, N. Miura, M. Naito, N. Kubota, and Y. Shiohara, Physica B 201, 266 (1994). 24. A.M. Gerrits, T.J.B.M. Janssen, A. Wittlin, N.Y. Chen, and P.J.M. van Bentum, Physica C 235-240, 1114 (1994). 25. J.E. Eldridge, C.H. Homes, J.M. WiUiams, A.M. Kini, and H.H. Wang, Spectrochimica Acta 51 A, 947 (1995). 26. F. Gao, G.L. Carr, CD. Porter, D.B. Tanner, S. Etemad, T. Venkatesan, A. Inam, B. Dutta, X.D. Wu, G.P. WilHams, and C.J. Hirschmugl, Phys. Rev. B 43, 10383 (1991). 27. F. Gao, G.L. Carr, CD. Porter, D.B. Tanner, G.P. Williams, C.J. Hirschmugl, B. Dutta, X.D. Wu, and S. Etemad, Phys. Rev. B 54, 700 (1996). 28. H.K. Ng and Y.J. Wang, in Proceedings of Physical Phenomena at High Magnetic Fields-II, edited by Z. Fisk, L.P. Gor'kov, D. Meltzer, and J.R. Schrieffer (World Scientific Press, Singapore, 1996). 29. T.R. Yang, S. Perkowitz, G.L. Carr, R.C Budhani, G.P. Williams, and CJ. Hirschmugl, Appl. Optics 29, 332 (1990). 30. J. Schutzmann, B. Gorshunov, K.F. Renk, J. Miinzel, A. Zibold, H.P. Geserich, A. Erb, and G. Muller-Vogt, Phys. Rev. B 46, 512 (1992).

PAGE 259

251 31. D.N. Basov, R. Liang, D.A. Bonn, W.N. Hardy, B. Dabrowski, M. Quijada, D.B. Tanner, J.P. Rice, D.M. Ginsberg, and T. Timusk, Phys. Rev. Lett. 74, 598 (1995). 32. K. Zhang, D.A. Bonn, S. Kamal, R. Liang, D.J. Baar, W.N. Hardy, D. Basov, and T. Timusk, Phys. Rev. Lett. 73, 2484 (1994). 33. M. Reedyk and T. Timusk, Phys. Rev. Lett. 69, 2705 (1992). 34. D.A. Bonn, P. Dosanjh, R. Liang, and W.H. Hardy, Phys. Rev. Lett. 68, 2390 (1992). 35. D.B. Romero, CD. Porter, D.B. Tanner, L. Forro, D. Mandrus, L. Mihaly, G.L. Carr, and G.P. Williams, Phys. Rev. Lett. 68, 1590 (1992). 36. K.A. Delin and A.W. Kleinsasser, Supercond. Set. Technol. 9, 227 (1996) 37. K. Kamaras, S.L. Herr, CD. Porter, N. Tache, D.B. Tanner, S. Etemad, T. Venkatesan, E. Chase, A. Inam, X.D. Wu, M.S. Hegde, and B. Dutta, Phys. Rev. Lett. 64, 84 (1990). 38. M. Golosovsky, M. Tsindlekht, and D. Davidov, Supercond. Sci. Technol. 9, 1 (1996) . 39. E. Demircan, P. Ao, and Q. Niu, Phys. Rev. B 54, 10027 (1996). 40. C. Caroli, P.G. de Gennes, and J. Matricon, Phys. Lett. 9, 307 (1964). 41. C. Caroli and J. Matricon, Phys. Kondens. Mater. 3, 380 (1965). 42. J. Bardeen and M.J. Stephen, Phys. Rev. 140, A1197 (1965). 43. L, Kramer and W. Pesch, Z. Phys. 269, 59 (1974). 44. W. Pesch and L. Kramer, J. Low Temp. Phys. 15, 367 (1973). 45. F. Gygi and M. Schluter, Phys. Rev. B 43, 7609 (1991). 46. S.G. Doettinger, R.P. Huebener, and S. Kittelberger, Phys. Rev. B 55, 6044 (1997) . 47. L Maggio-Aprile, Ch. Renner, A. Erd, E. Walker, and 0. Fischer, Phys. Rev. Lett. 75, 2754 (1995). 48. P.L Soininen, C. Kallin, and A.J. Berlinsky, Phys. Rev. B 50, 13883 (1994).

PAGE 260

252 49. Y. Ren, J.-H. Xu, and C.S. Ting, Phys. Rev. Lett. 74, 3680 (1995). 50. A.J. Berlinsky, A.L. Fetter, M. Franz, C. Kallin, eind P.I. Soininen, Phys. Rev. LeU. 75, 2200 (1995). 51. N.B. Kopnin and G.E. Volovik, (preprint) (1997). 52. E.-J. Choi, H.-T.S. Lihn, S. Kaplan, S. Wu, H.D. Drew, Qi Li, D.B. Fenner, J.M. Phillips, and S.Y. Hou, Physica C 254, 258 (1995). 53. H.-T.S. Lihn, E.-J. Choi, S. Kaplan, H.D. Drew, Qi Li, and D.B. Fenner, Phys. Rev. B 53, 927 (1996). 54. H.-T.S. Lihn, S. Wu, H.D. Drew, S. Kaplan, Qi Li, and D.B. Fenner, Phys. Rev. Lett. 76, 3810 (1996). 55. E.H. Brandt, Phys. Rev. Lett. 67, 2219 (1991). 56. M.W. Coffey and J.R. Clem, Phys. Rev. Lett. 67, 386 (1991). 57. M. Tachiki, T.Koyama, and S. Takahashi, Phys. Rev. B 50, 7065 (1994). 58. M. Tinkham, in Far-infrared Properties of Solids, edited by S.S. Mitra «ind S. Nudehnan (Plenum, New York, 1970), p. 223. 59. B. Koch, H.P. Geserich, and T. Wolf, Solid State Commun. 71, 495 (1989). 60. D.J. Bishop, P.L. Gammel, D.A. Huse, cind C.A. Murray, Science 255, 165 (1992). 61. K.H. Fischer, Superconductivity Review 1, 153 (1995). 62. B.G. Levi, Phys. Today 49, 7 (1996). 63. W.W. Warren, Jr., R.E. Walstedt, G.F. Brennert, R.J. Cava, R. Tycko, R.F. Bell, and G. Dabbagh, Phys. Rev. Lett. 62, 1193 (1989). 64. H. Alloul, T. Ohno, and P. Mendels, Phys. Rev. Lett. 63, 1700 (1989). 65. Y. Yoshinari, H. Yasuoka, Y. Ueda, K. Koga, and K. Kosuge, J. Phys. Soc. Japan 59, 3698 (1990). 66. M. Takigawa, A.P. Reyes, P.C. Hammel, J.D. Thompson, R.H. Heffner, Z. Fisk, and K.C. Ott, Phys. Rev. B 43, 247 (1991).

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253 67. J. Rossat-Nignod, L.P. Regnault, C. Vettier, P. Bourges, P. Biirlet, J. Bossy, J.Y. Henry, and G. Lapertot, Physica C 185-189, 86 (1991). 68. J.M. Tranquada, P.M. Gehring, G. Shirane, S. Shamoto, and M. Sato, Phys. Rev. B 46, 5561 (1992). 69. B. Bucher, P. Steiner, J. Karpinski, E. Kaldis, and P. Wachter, Phys. Rev. Lett. 70, 2012 (1993). 70. B. Batlogg, H.Y. Hwang, H. Takagim R.J. Cava, H.L. Kao, and J. Kwo, Physica C 235-240, 130 (1994). 71. T. Ito, K. Takenaka, and S. Uckida, Phys. Rev. Lett. 70, 3995 (1993). 72. A.G. Loeser, D.S. Dessau, and Z.-X. Shen, Physica C 263, 208 (1996). 73. D.S. Marshall, D.S. Dessau, A.G. Loeser, C.-H. Park, A.Y. Matsuura, J.N. Eckstein, I. Bozovic, P. Fournier, A. Kapitulnik, W.E. Spicer, and Z.-X. Shen, Phys. Rev. Lett. 76, 4841 (1996). 74. H. Ding, A.F. Belhnan, J.C. Campuzano, M. Randeria, M.R. Norman, T. Yokoya, T. Takahashi, H. Katayama-Yoshida, T. Mochiku, K. Kadowaki, G. Jennings, and G.P. Brivio, Phys. Rev. Lett. 76, 1553 (1996). 75. C.C. Homes, T. Timusk, R. Liang, D.A. Bonn, and W.N. Hardy, Phys. Rev. Lett. 71, 1645 (1993). 76. C.C. Homes, T. Timusk, D.A. Bonn, R. Liang, and W.N. Hardy,P/iystca C 254, 265 (1995). 77. D.N. Basov, A.V. R.A. Hughes, T. Strach, J. Preston, T. Timusk, D.A. Bonn, R. Liang, and W.N. Hardy, Phys. Rev. B 49, 12165 (1994). 78. A. Puchkov, D.N. Bosov, and T. Timusk, J. Phys. Condens. Matter 8, 10049 (1996). 79. D.N. Basov, R. Liang, B. Dabrowski, D.A. Bonn, W.N. Hardy, and T. Timusk, Phys. Rev. Lett. 77, 4090 (1996). 80. A. V. Puchkov, D.N. Basov, and T. Timusk, J. Phys.: Condens. Matter 8, 10049 (1996). 81. CM. Varma, P.B. Littlewood, S. Schmitt-rink, E. Abrahaxns, and A.E. Ruckenstein, Phys. Rev. Lett. 63, 1996 (1989). 82. P.B. Littlewood, and CM. Varma, J. Appl. Phys. , 69, 4979 (1991).

PAGE 262

254 83. T. Tamegai, K. Koga, K. Suzuki, M. Ichihara, F. Sakai, and Y. lye, Jpn. J. Appl. Phys. 28, L112 (1989). 84. N.L. Wang, B. Buschinger, C. Geibel, and F. Steglich, Phys. Rev. B 54, 7445 (1996). 85. K. Takenaka, Y. Imanaka, K. Tamasaku, T. Ito, and S. Uchida, Phys. Rev. B 46, 5833 (1992). 86. L.M. PauUus, B.W. Lee, M.B. Maple, and P.K. Tsai, Physica C 230, 255 (1994). 87. H. Takagi, B. Batlogg, H.L. Kao, J. Kwo, R.J. Cava, J.J. Krajewski, and W.F. Peck, Jr., Phys. Rev. Lett. 69, 2975 (1992). 88. Y. Nakamura and S. Uchida, Phys. Rev. B 47, 8369 (1993). 89. S. Tajima, H. Ishii, T. Nakahashi, T. Takagi, S. Uchida, M. Seki, S. Sugai, Y. Hidaka, M. Suzuki, T. Murakami, K. Oka, and H. Unoki, J. Opt. Soc. Am. , B 6, 475 (1989). 90. F. Wooten, in Optical Properties of Solids (Accidemic, New York, 1972). 91. S. Uchida, T. Ido, H. Takagi, T. Arima, and Y. Tokura, Phys. Rev. B 43, 7942 (1991). 92. J. Orenstein, G.A. Thomas, A.J. Millis, S.L. Cooper, D.H. Rapkine, T. Timusk, L.F. Schneemeyer, and J.V. Waszczak, Phys. Rev. B 42, 6342 (1990). 93. S.L. Cooper and K.E. Gray in Physical properties of High Temperature Superconductors IV, edited by D.M. Ginsberg (World Scientific, Singapore, 1993) p. 69. 94. M. Tinkham and R.A. Ferrell, Phys. Rev. Lett. 2, 331 (1959). 95. A. P. Litvinchuk, C. Thomsen, and M. Cardona in Physical properties of High Temperature Superconductors IV, edited by D.M. Ginsberg (World Scientific, Singapore, 1993) p. 375. 96. T. Egami ajid S.J.L. Billinge, in Physical Properties of High Temperature Superconductors V, edited by D.M. Ginsberg (World Scientific Press, Singapore, 1995) p.265. 97. A. Virosztek, and J. Ruvalds, Phys. Rev. B 42, 4064 (1990). 98. C.T. Rieck, W.A. Little, J. Ruvald, and A. Virosztek, Phys. Rev. B 51, 3772 (1995).

PAGE 263

255 99. P. Monthotix and D. Pines, Phys. Rev. B 49, 4261 (1994). 100. V.J. Emery, S.A. Kivelson, and H.Q. Liu, Phys. Rev. Lett. 64, 475 (1990).: V.J. Emery and S.A. Kivelson, Physica C 209, 597 (1993). 101. F. Gao, D.B. Romero, D.B. Taimer, J. Talvacchio, and M.G. Forrester, Phys. Rev. B 47, 1036 (1993). 102. P.B. Allen, T.P. Beaulac, F.S. Khan, W.H. Butler, F.J. Pinski, and J.C. Swihart, Phys. Rev. B 34, 4331 (1986). 103. I. Francois, C. Jaekel, G. Kyas, D. Dierickx, 0. Van der Biest, R.M. Keeres, V.V. MoshchaJkov, Y. Bruynseraede, H. G. Roskos, G. Borghs, and H. Kurz, Phys. Rev. B 53, 12502 (1996). 104. C. Ludwig, Q. Jiang, J. Kuhl, and J. Zegenhagen, Physica C 269, 249 (1996). 105. R.E. Glover and M. Tinkham, Phys. Rev. B 107, 844 (1956).; Phys. Rev. B 108, 243 (1957). 106. G. Brandi and A.J. Sievers, Phys. Rev. 5, 3350 (1972). 107. M.A. Quijada, D.B.Tanner, R.J. Kelley, and M. Onellion, Z. Phys. B 94, 255 (1994). 108. T. Pham, H.D. Drew, S.H. Moseley, and J.Z. Liu, Phys. Rev. B 44, 5377 (1991). 109. P.J. Hirsckfeld, W.O. Putikka, and D.J. Scalapino, Phys. Rev. Lett. 71, 3705 (1993). 110. D.J. Scalapino, Phys. Rep. 250, 329 (1995). 111. M.A. Quijada, D.B. Tanner, F.C. Chou, D.C. Johnston, and S.-W. Cheong, Phys. Rev. B 52, 15485 (1995). 112. A. Zibold et al. (to appear in Phys. Rev. B) (1997). 113. For the reference see R.M. Hazen, in Physical Properties of High Temperature Superconductors II, edited by D.M. Ginsberg (World Scientific Press, 1990) p.l21. 114. Y.-D. Yoon, Ph.D. Dissertation, Department of Physics, University of Florida, Gainesville (1995). 115. A.V. Puchkov, P. Foumier, T. Timusk, and N.N. Kolesnikov, Phys. Rev. LeU. 77, 1853 (1996).

PAGE 264

256 116. H. Ding, M.R. Norman, T. Yokoya, T. Takeuchi, M. Randeria, J,C. Campuzaino, T. Takahashi, T. Mocjiku, and K. Kadowaki, Phys. Rev. Lett. 78, 2628 (1997). 117. Y.J. Uemura, G.M. Luke, B.J. Sternlieb, J.H. Brewer, J.F. Carolan, W.N. Hardy, R. Kadono, J.R. Kempton, R.F. Kiefl, S.R. Kreitzman, P. Mulhem, T.M. Risemcin, D.Ll. Williams, B.X. Yang, S. Uchida, H. Takagi, J. GopalaJcrishnan, A.W. Sleight, M.A. Subramanian, C.L. Chien, M.Z. Cieplak, Gang Xiao, V.Y. Lee, B.W. Statt, C.E. Stronach, W.J. Kossler, and X.H. Yu, Phys. Rev. Lett. 62, 2317 (1989). 118. Y.J. Uemura, L.P. Le, G.M. Luke, B.J. Sternlieb, W.D. Wu, J.H. Brewer, T.M. Risemaji, C.L. Seaman, M.B. Maple, M. Ishikawa, D.G. Hinks, J.D. Jorgensen, G. Saito, and H. Yamochi, Phys. Rev. Lett. 66, 2665 (1991). 119. Y.J. Uemura, A. Keren, L.P. Le, G.M. Luke, W.D. Wu, Y. Kubo, T. Manako, Y. Shimakawa, M. Subramanian, J.L. Cobb, cind J.T. Mcirkert, Nature 364, 605 (1993). 120. Ch. Niedermayer, C. Bernhard, U. Binninger, H. Gliickler, J.L. Tallon, E.J. Ansaldo, and J.L Budnick, Phys. Rev. Lett. 71, 1764 (1993). 121. T.A. Friedmann, M.W. Rabin, J. Giapintzakis, J.R. Rice, and D.M. Ginsberg, Phys. Rev. B 42, 6217 (1990). 122. U. Welp, S. Fleshier, W.K. Kwok, J. Downey, Y. Fang, G.W. Crabtree, and J.Z. Liu, Phys. Rev. B 42, 10189 (1990). 123. R. Gagnon, C. Lupien, and L. Taillefer, Phys. Rev. B 50, 3458 (1994). 124. Z. Schlesinger, R.T. Collins, F. Holtzberg, C. Field, S.H. Blanton, U. Welp, G.W. Crabtree, Y. Fang, and J.Z. Liu, Phys. Rev. Lett. 65, 801 (1990). 125. L.D. Rotter, Z. Schlesinger, R.T. Collins, F. Holtzberg, C. Field, U. Welp, G.W. Crabtree, J.Z. Liu, Y. Fang, G. Vandervoort, and S. Fleshier, Phys. Rev. Lett. 67, 2741 (1991). 126. S.L. Copper, A. Kotz, M.A. Karlow, M.V. Kelin, W.C. Lee, J. Giapintzakis, and D.M. Ginsberg, Phys. Rev. B 45, 2549 (1992). 127. W.E. Pickett, H. Krakauer, R.E. Cohen, and D. J. Singh, Science 255, 46 (1992). 128. C.G. Olson, R. Liu, D.W. Lynch, R.S. List, A.J. Arko, B.W. Veal, Y.C. Chang, P.Z. Jiang, and A.P. Paulikas, Phys. Rev. B 42, 381 (1990).

PAGE 265

257 129. D.S. Dessau, Z.-X. Shen, D.M. King, D.S. Marshall, L.W. Lombardo, P.H. Dickenson, A.G. Loeser, J. DiCarlo, C.-H. Park, A. Kapitulnik, and W.E. Spicer, Phys. Rev. Lett. 71, 2781 (1992). 130. Z.-X. Shen, D.S. Dessau, B.O. Wells, D.M. King, W.E. Spicer, A.J. Arko, D. Mjirshall, L.W. Lombardo, A. Kapitulnik, P. Dickinson, S. Doniach, J. Dicarlo, A.G. Loeser, and C.H. Park, Phys. Rev. Lett. 70, 1553 (1993). 131. R.J. Kelly, Jian Ma, G. Margciritondo, ajid M. Onellion, Phys. Rev. Lett. 71, 4051 (1993). 132. P. Aebi, J. Osterwjilder, P. Schwaller, L. Schlapbach, M. Shimoda, T. Mochiku, and K. Kadowaki, Phys. Rev. Lett. 72, 2757 (1994). 133. Z.-X. Shen, and D.S. Dessau, Phys. Rep. 253, 1 (1995). 134. H. Ding, J.C. Campuzano, A.F. Bellman, T. Yokoya, M.R. Norman, M. Randeria, T. Takadiashi, H. Katayama-Yoshida, T. Mochiku, K. Kadowaki, and G. Jennings, Phys. Rev. Lett. 74, 2784 (1995). 135. Jian Ma, C. Quitmann, R.J. Kelly, H. Berger, G. Mairgaritondo, and M. Onellion, Science 267, 862 (1995). 136. A.P. Kampf, and J.R. Schrieffer, Phys. Rev. B 41, 6399 (1990).; Phys. Rev. B 42, 7967 (1990). 137. T. Yokoya, T. Takahashi, T. Mochiku, and K. Kadpwaki, Phys. Rev. B 53, 14055 (1996). 138. H.Ding, M.R. Norman, J.C. Campuzano, M. Randeria, A.F. Bellman, T. Yokaya, T. Takahashi, T. Mochiku, and K. Kadowaki, Phys. Rev. B 54, 9678 (1996). 139. J. Kane, Q. Chen, and K.-W. Ng, Phys. Rev. Lett. 72, 128 (1994). 140. T.P. Devereaux, D. Einzel, B. Stadlober, R. Hackl, D.H. Leach, and J.J. Neumeier, Phys. Rev. Lett. 72, 396 (1994). 141. M.A. Quijada, Ph.D. Thesis, Department of Physics, University of Florida (1994). 142. H. Heinrich, G. Kostorz, B. Heeb and L.J. Gauckler, Physica C 224, 133 (1994). 143. Jian Ma, P. Ahneras, R.J. Kelly, H. Berger, G. Margaritondo, X.Y. Cai, Y. Feng, M. Onellion, Phys. Rev. B 51, 9271 (1995). 144. P.D. Han, and D.A. Payne, J. Crystal Growth 104, 201 (1990).

PAGE 266

258 145. D.B. Mitzi, L.W. Lombardo, A. Kapitulunik, S.S. Laderman, and R.D. Jacowitz, Phys. Rev. B 41, 6564 (1990). 146. M.D. Kirk, J. Nogami, A.A. Baski, D.B. Mittzi, A. Kapitulnik, T.H. Geballe, and C.F. Quate, Science 242, 1673 (1988). 147. R.M. Heizen, in Physical Properties of High Temperature Superconductors II, edited by D.M. Ginsberg (World Scientific Press, 1990) p.l29. 148. L. Winkeler, S. Seidewasser, B. Beschoten, H. Frank, F. Nouvertne, G. Guntherodt, Physica C 265, 194 (1996). 149. X.L. Wu, Z. Zhang, Y.L. Wang, and CM. Lieber, Science 248, 1211 (1990). 150. I. Terasaki, S. Tajima, H. Eisaki, H. Takagi, K. Uchinokura, and S. Uchida, Phys. Rev. B 41, 865 (1990).. 151. M.K. Kelly, P. Barboux, J.-M. Tarascon, and D.E. Aspnes, Phys. Rev. B 40, 6797 (1989). 152. Yun-Yu Wang, and A.L. Ritter, Phys. Rev. B 43, 1241 (1991). 153. D.M. Ori, A. Goldoni, U. del Pennino, and F. Parmigiani, Phys. Rev. B 52, 3727 (1995). 154. M.K. Kelly, P. Barboux, J.-M. Tarascon, D.E. Aspnes, P.A. Morris, and W.A. Bonner, Physica C 162-164, 1123 (1989). 155. D.B. Romero, G.L. Carr, and D.B. Tanner, L. Forro, D. Mandrus, L. Mihaly, and G.P. WilHams, Phys. Rev. B 44, 2818 (1991). 156. T. Ito, H. Takagi, S. Ishibashi, T. Ido, and S. Uchida, Nature 350, 596 (1991). 157. S. Martin, A.T. Fiory, R.M. Fleming, L.F. Schneemeyer, and J.V. Waszczak, Phys. Rev. Lett. 60, 2194 (1988). 158. J.M. Wheatley, T.C. Hsu, and P.W. Anderson, Nature 333, 121 (1988). 159. J.M. Wheatley, T.C. Hsu, and P.W. Anderson, Phys. Rev. B 37, 5897 (1988). 160. P.W. Anderson and Z. Zou, Phys. Rev. Lett. 60, 132 (1988), 161. X.-D. Xiang, S. Mckeman, W.A. Vareka, A. Zettl, J.L. Corkill, T.W. Barbee HI, and M.L. Cohen, Nature 348, 145 (1990).

PAGE 267

259 162. X.-D. Xiang, W.A. Vareka, A. Zettl, J.L. Corkill, T.W. Barbee III, M.L. Cohen, N. Kijima, and R. Gronsky, Science 254, 1487 (1991). 163. X.-D. Xiang, A. Zettl, W.A. Vareka, J.L. Corkill, T.W. Barbee III, and M.L. Cohen, Phys. Rev. B 43, 11496 (1991). 164. X.-D. Xiang, W.A. Vareka, A. Zettl, J.L. Corkill, M.L. Cohen, N. Kijima, and R. Gronsky, Phys. Rev. Lett. 68, 530 (1992). 165. D. Pooke, K. Kishio, T. Koga, Y. Fukuda, N. Sanada, M. Nagoshi, and K. Yamafuji, Physica C 198, 349 (1992). 166. J.-H. Choy, S.-G. Kang, D.-H. Kim, and S.-J. Hwang, J. Solid State Chem. 102, 284 (1993). 167. T. Huang, M. Itoh, J. Yu, Y. Inaguma, and T. Nakamura, Phys. Rev. B 49, 9885 (1994). 168. J. Ma, P. Almeras, R.J. Kelley, H. Berger, G. Margaritondo, A. Umezawa, M.L. Cohen, and M. Onellion, Physica C 227, 371 (1994). 169. A. Fujiwaia, Y. Koike, K. Sasaki, M. Mochida, T. Noji, and Y. saito, Physica C 203, 411 (1992). 170. T. Kluge, A. Fujiwara, M. Kato, and Y. Koike, Phys. Rev. B 54, 86 (1996). 171. J.-H. Choy, S.-G. Kang, D.-H. Kim, and N.-H. Hur, in Superconducting Materials, edited by J. Etotirneau, J.-B. Torrance, and H. Yamauchi (IITT International, Paris, 1993) p. 335. 172. E. Faulques and R.E. Russo, Solid State Commun. 82, 531 (1992). 173. C.H. Qiu, S.P. Ahrenkiel, N. Wada, and T.F. Ciszek, Physica C 185, 825 (1991). 174. J. Prade, A.D. Kulkami, F.W. de Wette, U. Schroder, and W. Kress, Phys. Rev. B 39, 2771 (1989). 175. I. Terasaki, (impublished). 176. W. Gabes and D.J. Stufkens, Spectrochimica Acta 30A, 1835 (1974). 177. M.A. Abkowitz, J.W. BriU, P.M. Chaikin, A.J. Epstein, M.F. Froix, C.H. Griffiths, W. Gimning, A.J. Heeger, W.A. Little, J.S. Miller, M. Novatny, D.B. Tanner, and M.L. Slade, Annals New York Academy of Science 313, 459 (1978). 178. L. Andrews, E.S. Prochaska, and A. Loewenschuss, Inorg. Chem. 19, 463 (1980).

PAGE 268

260 179. D.B. Romero, CD. Porter, D.B. Tanner, L. Forro, D. Mandrus, L. Mihaly, G.L. Carr, and G.P. Williams, Solid State Commun. 82, 183 (1992). 180. D.B. Tanner, D.B. Romero, K. Kamaras, G.L. Carr, L. Forro, D. Maindrus, L. Mihaly, and G.P. Williams, in HighTemperature Superconductivity, edited by J. Ashkenazi (Plenum Press, New York, 1991) p. 159. 181. S. Mau-tin, A.T. Fiory, R.M. Fleming, G.P. Espinosa, and A.S. Cooper, Appl. Phys. Lett. 54, 72 (1989). 182. J.T. Maxkert, Y. Dcilichaouch, and M.B. Maple in Physical properties of High Temperature Superconductors I, edited by D.M. Ginsberg (World Scientific, Singapore, 1989) p. 265. 183. A.A. Abrikosov and L.P. Gor'kov, Zh. Eksp. Teor. Fiz. 35, 1558 (1950); Sov. Phys. JETP 8, 1090 (1959). 184. P.W. Anderson, J. Phys. Chem. Solids 11, 26 (1959). 185. C. Quitmann, P. Almeras, Jian Ma, R.J. Kelley, H. Berger, Cai Xueyu, G. Margaritondo, and M. Onellion, Phys. Rev. B 53, 6819 (1996). 186. H. Eisaki and S. Uchida, J. Phys. Chem. Solids 56, 1811 (1995). 187. A.A. Tesvetkov, J. Schutzmann, J.I. Gorina, G.A. Kcdjushnaia, tind D. van der Marel, (to be published) (1997). 188. M. Reedyk, Ph.D. Thesis, Mcmaster University (1992). 189. A.V. Puchkov, T. Timusk, S. Doyle, and A.M. Hermann, Phys. Rev. B 51, 3312 (1995). 190. J.-T. Kim, T.R. Lemberger, S.R. Foltyn, and X. Wu, Phys. Rev. B 49, 15790 (1994). 191. D.N. Basov et al, (unpublished). 192. A. Gold, S.J. Allen, B.A. Wilson, and D.C. Tsui, Phys. Rev. B 25, 3519 (1982). 193. H.K. Ng, M. Capizzi, G.A. Thomas, R.N. Bhatt, and A.C. Gossard, Phys. Rev. B 33, 7329 (1986). 194. H.F. Jang, G. Cripps, and T. Timusk, Phys. Rev. B 41, 5152 (1990). 195. K. Lee, R. Menon, CO. Yoon, and A.J. Heeger, Phys. Rev. B 52, 4779 (1995).

PAGE 269

261 196. P.B. AUen, Phys. Rev. B 3, 305 (1971). 197. C.C. Homes, Q. Song, B.P. dayman, D.A. Bonn, R. Liang, and W.N. Hardy, SPIE Proceedings 2696, 82 (1996). 198. M.J. Simmer, J.-T. Kim, and T.R. Lemberger, Phys. Rev. B 47, 12248 (1993). 199. E.R. Ulm, J.-T. Kim, T.R. Lemberger, S.R. Foltyn, and Xindi Wu, Phys. Rev. B 51, 9193 (1995). 200. A.V. Mahajan, H. AUoul, G. Collin, and J.F. Marucco, Phys. Rev. Lett. 72, 3100 (1994). 201. P. Mendels, H. Alloul, G. Collin, N. Blanchard, J.F. Marucco, and J. Bobroff, Physica C 235-240, 1595 (1994). 202. D.A. Bonn, S. Kamal, K. Zhang, R. Liang, D.J. Baar, E. Klein, and W.N. Hardy, Phys. Rev. B 50, 4051 (1994). 203. S.S.P. Parkin, E.M. Engler, R.R. Schumaker, R. Lagier, V.Y. Lee, J.C. Scott, and R.J. Greene, Phys. Rev. Lett. 50, 270 (1983). 204. J.M. Williams, J.R. Ferraro, R.J. Thorn, K.D. Carlson, U. Geiser, H.H. Wang, A.M. Kini, and M.-H. Whangbo, Organic Superconductors (Including Fullerenes): Synthesis, Structure, Properties and Theory (Prentice Hall, Englewood Cliffs, New Jersey, 1992). 205. J.M. Williams, A.M. Kini, H.H. Wang, K.D. Carlson, U. Geiser, L.K. Montgomery, G.J. Pyrka, D.M. Watkins, J.M. Konmiers, S.J. Boryschnk, A.V. Strieby Crouch, W.K. Kwok, J.E. Schirber, D.L. Overmyer, D. Jtmg, and M.-H. Whangbo, Inorg. Chem. 29, 3272 (1990). 206. L.-K. Chou, M.A. Quijada, M.B. Clevenger, G.F. de Oliveira, K.A. Abboud, D.B. Tanner, and D.R. Talham, Chem. Mater. 7, 531 (1995). 207. H. Kobayashi, R. Kato, T. Mori, A. Kobayashi, Y. Sasaki, G. Saito, and H. Inokuchi, Chem. Lett. 759 (1983). 208. H. Kobayashi, T. Mori, R. Kato, A. Kobayashi, Y. Sasaki, G. Saito, and H. Liokuchi, Chem. Lett. 581 (1983). 209. X. Bu, L Cisarova, and P. Coppens, Acta Cryst. C48, 516 (1992). 210. X. Bu, L Cisarova, and P. Coppens, Acta Cryst. C48, 1563 (1992).

PAGE 270

262 211. K.A. Abbound, L.-K. Chou, M.B. Clevenger, G.F. Oliveira, and D.R. Talham, Acta Cryst. C51, 2356 (1995). 212. X. Bu, I. Cisarova, and P. Coppens, Acta Cryst. C48, 1558 (1992). 213. X. Bu, I. Cisarova, and P. Coppens, Acta Cryst. C48, 1562 (1992). 214. P. Prere, R. Carlier, K. Boubekeur, A. Gorgues, J. Roncali, A. Tjillec, M. Jubault, and P. Batail, J. Chem. Soc, Chem. Commun. 2071 (1994). 215. J. Larsen and C. Lenoir, Synthesis 2, 134 (1988). 216. G.M. Sheldrick, SHELXTL5 (Nicolet XRD Corporation, Madison, Wisconsin, 1995). 217. J.G. Vegter, T. Hibma, and J. Konamandeur, Chem. Phys. Lett. 3, 427 (1969). 218. G.J. Kramer, J.C. Jol, H.B. Brom, L.R. Groeneve, and J. Reedijk, J. Phys. C 21, 4591 (1988). 219. M.J. Rice, Phys. Rev. Lett. 37, 36 (1976). 220. M.J. Rice, Solid State Commun. 31, 93 (1979). 221. M.J. Rice, V.M. Yartsev, and C.S. Jacobsen, Phys. Rev. B 21, 3437 (1980). 222. D.B. Tanner, in Extended Linear Chain Compounds, edited by J.S. Miller (Plenum, New York, 1982), Vol. 2, Chap. 5. 223. H. Tajima, K. Yakushi, H. Kuroda, £ind G. Seiito, Solid State Commun. 56, 159 (1986). 224. K. Yakushi, H. Tajima, H. Kanbara, M. Tcimtira, H. Kuroda, G. S«iito, H. Kobayahi, R. Kato, and A. Kobayashi, Proceedings of the Fifteenth Yamada Conference on Physics and Chemistry of Quasi OneDimensional Conductors, Physica B 143, 463 (1986). 225. H. Kuroda, K. Yakushi, H. Tajima, A. Ugawa, M. Tamura, Y. Okawa, and A. Kobayashi, Synth. Met. 27, A491 (1988). 226. F.E. Mabbs and D.J. Machin, Magnetism and Transition Metal Complexes (Chapman and Hall, London 1973). 227. A.B. Harris and R.V. Lange, Phys. Rev. 157, 295 (1967). 228. M.J. Rice, Solid State Commun. 31, 93 (1979).

PAGE 271

263 229. R. Hoffmann, J. Chem. Phys. 39, 1397 (1963). 230. J. Ammeter, H.-B. Burgi, J. Thibeault, and R. Hoffmann, J. Am. Chem. Soc. 100, 3686 (1978). 231. E. Clementi and C. Roetti, At. Nucl. Data Tables 14, 177 (1974). 232. (a) M.-H. Whangbo, J.M. Williams, P.C.W. Leung, M.A. Beno, T.J. Emge, and H.H. Wang, Inorg. Chem. 24, 3500 (1985). 233. M. Meneghetti, R. Bozio, and C. Pedle, J. Physique (Paris) 47, 1377 (1986). 234. M.E. Kozlov, K.I. Pokhodnia, and A. A. Yurchenko, Spectrochimica Acta 43A, 323 (1987). 235. M.E. Kozlov, K.I. Pokhodnia, and A. A. Yurchenko, Spectrochimica Acta 45A, 437 (1989). 236. J.R. Ferraro, H.H. Waag, J. Ryan, and J.M. Williams, Applied Spectroscopy 41, 1377 (1987). 237. C.S. Jacobsen, D.B. Tanner, J. M. Willicims, U. Geiser, and H.H. Wang, Phys. Rev. B 35, 9605 (1987). 238. K. Komelsen, J.E. Eldridge, C.C. Homes, H.H. Wang, and J.M. Williams, Solid State Commun. 72, 475 (1989). 239. K. Kornelsen, J.E. Eldridge, H.H. Wang, and J.M. Williams, Phys. Rev. B 44, 5235 (1991). 240. J.E. Eldridge, K. Kornelsen, H.H. Wang, J.M. WiUiams, A.V.S. Crouch, and D.M. Watkins, Solid State Commun. 79, 583 (1991). 241. 0.0 Drozdova, V.N. Semkin, R.M. Vlasova, N.D. Kushch, and E.B. Yagubskii, Synth. Met. 64, 17 (1994). 242. V.M. Yartsev and C.S. Jacobsen, Phys. Status Solidi B125, K149 (1988). 243. R. Bozio and C. Pecile, J. Phys. C 13, 6205 (1980). 244. R. Bozio and C. Pecile, Solid State Commun. 37, 193 (1981). 245. J.W. Bray, L.V. Interrante, I.S. Jacobs, and J.C. Bonner, in Extended Linear Chain Compounds, edited by J.S. Miller (Plenum, New York, 1983), Vol. 3, Chap. 7.

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264 246. J.W. Bray, H.R. Hart Jr., L.V. Interrante, I.S. Jacobs, J.S. Kasper, G.D. Watkins, S.H. Wee, and J.C. Bonner, Phys. Rev. Lett. 35, 744 (1975). 247. I.S. Jacobs, J.W. Bray, H.R. Hart Jr., L.V. Interrante, J.S. Kasper, G.D. Watkins, D.E. Prober, and J.C. Bonner, Phys. Rev. B 14, 3036 (1976). 248. S. Huizinga, J. Kommandeur, G.A. Sawatzky, B.T. Thole, K. Kopinga, W.J.M. de Jonge, and J. Roos, Phys. Rev. B 19, 4723 (1979). 249. S.D. OberteUi, R.H. Friend, D.R. Talham, M. Kurmoo, and P. Day, J. Phys. Condens. Matter 1, 5671 (1989). 250. C.S. Jacobsen, H.J. Pederson, K. Mortensen, and K. Bechgaard, J. Phys. C: Solid St. Phys. 13, 3411 (1980). 251. M. Hase, I. Terasaki, and K. Uchinokiira, Phys. Rev. Lett. 70, 3651 (1993). 252. L.N. Bulaevskii, Fiz. Tver. Tela 11, 1132 (1969). [Sov. Phys. Solid State 11, 921 (1969).] 253. E. Pytte, Phys. Rev. B 10, 4637 (1974). 254. A. Maaroufi, S. Flandrois, C. Cotdon, P. Delhaes, J.P. Morand, and G. Pillion, J. Physique Coll. 44, C3, 1091 (1983). 255. F. Creuzet, C. Boubonais, L.G. Caron, D. Jerome, and K. Bechgjiard, Synth. Met. 19, 289 (1984). 256. F. Creuzet, D. Jerome, and A. Moradpour, Mol. Cryst. Liq. Cryst. 119, 297 (1985). 257. M. Hase, I. Terasaki, K. Uchinokura, M. Tokimaga, N. Miura, and H. Obara, Phys. Rev. B 48, 9616 (1993). 258. J.P. Pouget, L.P. Regnault, M. Ain, B. Hennion, J.P. Renard, P. Veillet, G. Dhalenne, and A. Revcolevschi, Phys. Rev. Lett. 72, 4037 (1994). 259. J.L. Musfeldt, Y.J. Wang, S. Jandl, M. Poirier, A. Pevcolevschi, and G. Dhalenne, Phys. Rev. B 54, 469 (1996). 260. J. Ferraris, D.O. Cowan, V.J. Walatka, and J.H. Perlstein, J. Am. Chem. Sac. 95, 948, (1973). 261. K. Bechgaard, K. Carueiro, F.B. Rasmussen, G. Rindorf, C.S. Jacobsen, H.J. Pedersen, and J.C. Scott, J. Am. Chem. Soc. 103, 2440, (1981).; K. Bechgaard,

PAGE 273

265 C.S. Jacobsen, K. Mortensen, H.J. Pedersen, and N. Thorup, Solid State Commun. 33, 1119 (1980). 262. R.P. Shibaeva, V.F. Kaminskii, and E.B. Yagubskii, Mol. Cryst. Liq. Cryst. 119, 361 (1985).; H. Kobayashi, R. Kato, A. Kobayashi, Y. Nishio, K. Kajita, and W. Sasaki, Chem. Lett. 789, 833, 957, (1986). 263. P. Cassoux, L. Valade, H. Kobayashi, A. Kobayashi, R.A. Clark, and A.E. Underhill, Coord. Chem. Rev. 110, 115, (1991). 264. L. Brossard, M. Ribault, L. Valade, and P. Cassoux, Physica B 143, 378, (1986). 265. K. Kajita, Y. Nishio, S. Moriyama, R. Kato, H. Kobayashi, W. Sasaki, A. Kobayashi, H. Kim, and Y. Sasaki, Solid State Commun. 65, 361 (1988). 266. H. Tajima, M. Inokuchi, A. Kobayashi, T. Ohta, R. Kato, H. Kobayashi, and H. Kuroda, Chem. Lett. 1235, (1993). 267. A.E. Pullen, J. Piotraschke, K.A. Abboud, J.R. Reynolds, H.L. Liu, and D.B. Tanner, Polym. ,Mater. Sci. Eng. Symp. Proc. 72, 321, (1995). 268. T. Nakamura, A.E. Underbill, T. Coomber, R.H. Friend, H. Tajima, A. Kobayashi, and H. Kobayashi, Inorg. Chem. 34, 870, (1995).; T. Nakamura, A.E. Underbill, T. Coomber, R.H. Friend, H. Tajima, A. Kobayashi, and H. Kobayashi, Synth. Met. 70, 1061 (1995). 269. L. Valade, J.-P. Legros, M. Bousseau, P. Cassoux, M. Geirbauskas, and L.V. Interrante, J. ,Chem. Soc. Dalton Trans. 783, (1985). 270. R. Kato, H. Kobayashi, H. Kim, A. Kobayashi, Y. Sasaki, T. Mori, and H. Inokuchi, Synth. Met. 27, B359 (1988). 271. G.C. PapavassiHou, A.M. Cotsilios, and C.S. Jacobsen, J. Mol. Struc. 15, 41, (1984). 272. H. Tajima, T. Naito, M. Tamura, A. Kobayashi, H. Kuroda, R. Kato, H. Kobayashi, R.A. Clark, and A.E. Underbill, Solid State Commun. 79, 337 (1991). 273. H. Tajima, M. Tamura, T. Naito, A. Kobayashi, R. Kato, H. Kobayashi, R.A. Clark, and A.E. Underbill, Mol. Cryst. Liq. Cryst. 181, 233 (1990). 274. M. Tamura, R. Masuda, T. Naito, H. Tajima, H. Kuroda, A. Kobayashi, K. Yakushi, R. Kato, H. Kobayashi, M. Tokumoto, N. Kinoshita, and H. Anzai, Synth. Met. 41, 2499 (1991).

PAGE 274

266 275. C.S. Jacobsen, V.M. Yartsev, D.B. Tanner, and K. Bechgaard, Synth. Met. 55, 1925 (1993). 276. W.J. Barreto, M.C.C. Ribeiro, and P.S. Santos, J. Mol. Struc. 269, 75, (1992). 277. D.B. Tanner, in Extended Linear Chain Compounds, edited by J.S. Miller (Plenum, New York, 1982), Vol. 2, Chap. 5. 278. M.J. Rice, V.M. Yartsev, and C.S. Jacobsen, Phys. Rev. B 21, 3437 (1980). 279. G. Steimecke, H.J. Sieler, R. Kirmse, cind E. Hoyer, Phosphorus and Sulfur 7, 49, (1979). 280. Robertson Microlit Lab, Inc., Madison, N.J.. 281. G.M. Sheldrick, SHELXTL plus (Nicolet XRD Corporation: Madison, Wisconsin 1990). 282. F. Wooten, in Optical Properties of Solids (Academic, New York, 1972). 283. L. Valade, J.-P. Legros, and P. Cassoux, Mol. Cryst. Liq. Cryst. 140, 335 (1986). 284. D. Reefman, J. P. Cornelissen, J.G. Haasnoot, R.A.G. de Graafi, and J. Reedijk, Inorg. Chem. 29, 3933, (1990). 285. G.J. Kramer, J.C. Jol, H.B. Brom, L.R. Groeneve, and J. Reedijk, J. Phys. C 21, 4591, (1988). 286. A.J. Epstein, E.M. Conwell, D.J. Sandman, and J.S. Miller, Solid State Commun. 23, 355 (1977). 287. A.J. Epstein, E.M. Conwell, D.J. Sandman, and J.S. Miller, Solid State Commun. 24, 627 (1977). 288. U. Fano, Phys. Rev. 124, 1866 (1961). 289. J.M. Ziman, in Principles of the Theory of Solids, 2nd ed. (Cambridge University Press, Cambridge, England, 1972). 290. J. Hubbard, Phys. Rev. B 17, 494 (1978). 291. R.E. Peierls, in Quantum Theory of Solids (Oxford University Press, Lodon, England, 1955), p. 108. 292. S. Mazumdar, and Z.G. Soos, Phys. Rev. B 23, 2810 (1981).

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267 293. S. Mazumdar, and A.N. Bloch, Phys. Rev. Lett. 50, 207 (1983). 294. J.E. Hirsch, and D.J. Scalapino, Phys. Rev. Lett. 50, 1168 (1983). 295. A.S. Davydov, in Theory of Molecular Excitons (Plenum, New York, 1971). 296. D.P. Craig, and S.H. Walmsley, in Excitons in Molecular Crystals (Benjamin, New York, 1971). 297. A. Kobayashi, H. Kim, Y. Sasaki, R. Kato, and H. Kobayashi, Solid State Commun. 62, 57 (1987). 298. E. Canadell, S. Ravy, J.P, Pouget, and L. Brossaid, Solid State Commun. 75, 633 (1990). 299. V.M. Yartsev, Phys. Stat. Sol. B 126, 501, (1984); V.M. Yartsev, Phys. Stat. Sol. B 49, 157, (1988).

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BIOGRAPHICAL SKETCH Hsiang-Lin Liu weis bom in Taipei, Taiwan, on January 2, 1966. He is the eldest child of Fu-Sou Liu and Yj-Ying Tsai. He spent his entire childhood in Taipei where he graduated from the high school in 1984. That same year he entered the Tamkang University at Tcimsui, Taiwan, and graduated in 1988 with a bachelor's degree in physics. In August 1988, he started his graduate studies at Tsing Hua University, Hsinchu, Taiwan. There he worked with Professor Kenneth Wen-Kai Shung on the calculation of the electronic and optical properties of simple metal clusters by using density fimctional theory. He was awarded a master's degree in Jime 1990. FVom July 1990 to May 1992, he did the military service as a second lieuten«int. After dischcirge, he worked as a research assisteint in the Institute of Physics, Academia Sinica, Taiwan, where he took part in a project on the experimental surface physics. He was fortunate to have a Ph.D. admission to University of Florida in April 1993. He said farewell to his country, parents, girl friend (now is his wife) and aurived at Gainesville in July 25, 1993. He began doctoral research with Professor David B. Taimer in January 1994 to study optical properties of high-Tc superconductors. Hsiang-Lin is extremely happy that he will complete his doctoral studies in June 27, 1997. His first job as a Ph.D. will being July 15, 1997, at the University of Illinois at UrbeinaChampaign as a postdoctoral physicist in the research group of Professors Miles V. Klein and S. Lance Cooper. He is going to miss everything at the University of Florida but is ready to take the exciting challenges in his future. 268

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I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. David B. Tanner, Chairman Professor of Physics I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Ml \\\ 1 Peter J.^ lirshfeld Associate Professor of Physics I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. John M. Graybeal Associate Professor of Physics I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. David H. Reitze Assistant Professor of Physics

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I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. This dissertation was submitted to the Graduate Faculty of the Department of Physics in the College of Liberal Arts and Sciences and to the Graduate School and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy. August 1997 Dean, Graduate School

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I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. David B. Tanner, Chairman Professor of Physics I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Ml \\\ 1 Peter J.^ lirshfeld Associate Professor of Physics I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. John M. Graybeal Associate Professor of Physics I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. David H. Reitze Assistant Professor of Physics

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I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. This dissertation was submitted to the Graduate Faculty of the Department of Physics in the College of Liberal Arts and Sciences and to the Graduate School and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy. August 1997 Dean, Graduate School