Table Of ContentANISOTROPY IN THE INFRARED, OPTICAL
AND TRANSPORT PROPERTIES OF HIGH
TEMPERATURE SUPERCONDUCTORS
By
MANUEL ALBERTO QUIJADA
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
1994
UNIVERSITY OF FLORIDA LIBRARIES
ACKNOWLEDGMENTS
It is with great pleasure that I thank my advisor, Professor David B. Tanner,
for his advice, patience and encouragement throughout my graduate career here at
the University of Florida. I feel fortunate to be part of his research group. I also
thank Professors J. Graybeal, P.J. Hirschfeld, C. Hooper, N. Sullivan, and J.H. Sim-
mons for their interests in serving on my supervisory committee and for reading this
dissertation.
Thanks also go to all my past and present colleagues in Tanner's group for their
friendship, useful conversations and cooperation. In particular, I would like to thank
CD. Porter for his assistance with computer software. I am also indebted to Drs. G.L.
Carr, D.B. Romero, and V. Zelezny for many enlightening and useful discussions.
I would like to express my gratitude to Drs. J.P. Rice, D.M. Ginsberg, M. Kelley,
M. Onellion, F.C. Chou and D.C. Johnston for providing good quality single crystals
that were essential to the completion of this work.
The technical support of the staff members in the physics department machine
shop and engineers in the cryogenic group is appreciated greatly.
I would also like to take this opportunity to thank my wife, Zunilda, and my
daughter, Melissa, for their support and understanding during the countless nights
they stayed alone while I was working in the laboratory.
Finally, I also thank my parents for giving me their support throughout my aca-
demic
life.
Financial support from the NSF (grant number DMR 9101676) and from a U.S.
Department of Education fellowship are gratefully acknowledged.
11
TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS
ii
ABSTRACT
vii
CHAPTERS
INTRODUCTION
I. 1
REVIEW OF PREVIOUS EXPERIMENTAL WORK
II. 5
Crystal Structure of Copper-Oxide Materials 5
La2Cu04+5 5
YBa Cu
2 3 7_^ 8
Bi Sr CaCu208 10
2 2
Review of Optical Properties Copper-Oxide Materials 12
c-Axis Response 13
Midinfrared Absorption in the Cu0 Planes 15
2
Anisotropy in the ab Plane 19
YBa Cu
2 3 7_(5 19
Bi Sr CaCu 22
2 2 2 8
THEORY
III. 25
Models for Carriers in the Cu0 Planes: Normal State 25
2
Three-Band Hubbard Model 25
t - J Model 2S
Models for ffi (cu) 30
Numerical Results 30
Two-Component Model 33
One-Component Model 35
iii
Superconducting State Models 37
Symmetry of the Order Parameter 3S
Evidence for Proposed Pairing States 40
Determination of Gap by Optical Spectroscopy 43
IV. EXPERIMENTAL TECHNIQUES 45
Fourier Transform Infrared Spectroscopy 45
Optical Spectrometers 48
Bruker Fourier Transform Spectrometer 48
Bolometer Detector 49
The Perkin-Elmer Monochromator 50
Polarizers 54
Sample Mounting and Low Temperature Measurements 56
Normalization Procedure of the Reflectance 58
Data Analysis of the Spectra: The Kramers-Kronig Transformations 59
. .
High-Frequency and Low-Frequency Extrapolations 60
Optical Constants 61
Sample Preparation Techniques 62
YBa2Cu30 _^ Single-Domain Crystal 63
7
Bi2SroCaCu208 Single-Domain Crystals 65
La2Cu04+5 Single Crystal 67
V. OPTICAL STUDY OF La2Cu04+5 SINGLE CRYSTAL 69
c-Axis Reflectance of LaoCu044-5 72
Room Temperature Spectra 72
Low Temperature c-Axis Reflectance 74
Assignment c-Axis Phonons 76
Effective Charge SO
a6-Plane Reflectance 82
Assignment a6-Plane Phonons 82
Low Temperature at-Plane Reflectance S4
Results of a6-Plane Optical Constants 86
Loss Function 87
afr-Plane Optical Conductivity 89
iv
Midinfrared Component 90
Comparison of a6-Plane Reflectance: q c and q _L c 93
||
Concluding Remarks 97
VI. ANISOTROPY IN THE AB-PLANE OPTICAL PROPERTIES
OF YBa Cu _£ 99
2 3 7
Room Temperature Spectra 99
Temperature Dependent Reflectance 103
Effect of the Chains 107
a6-Plane Anisotropy in the London Penetration Depth 109
VII. ANISOTROPY IN THE AB-PLANE OPTICAL PROPERTIES
OF Bi Sr CaCu 08 Ill
2 2 2
Results of the Optical Reflectance 113
Room Temperature Spectra 113
Temperature Dependent Spectra 114
Discussion of Optical Constants 116
Temperature Dependent Optical Conductivity 121
One-Component Analysis 125
Two-Component Analysis 127
Drude Component 129
Midinfrared Absorption 134
Superconducting Condensate 139
a6-Plane Anisotropy in the London Penetration Depth 141
Optical Conductivity and Symmetry of the Order Parameter 143
VIII. RESISTIVITY TENSOR OF Bi Sr CaCu SINGLE-DOMAIN
2 2 2 8
CRYSTALS
147
Sample Preparation and Measurement Method 148
Resistivity Analysis for Anisotropic Materials 152
Resistivity Tensor 158
c-Axis Results 158
Anisotropy in the a&-Plane Resistivity 159
Temperature Dependent a6-Plane Resistivity 160
v
Closer Look to the Transition Temperature 161
Results and Discussion 163
Review of Flux-Flow Resistance and Kosterlitz-Thouless Transition 165
.
Concluding Remarks 168
CONCLUSIONS
IX. 170
APPENDICES
A OPTICAL STUDY OF BEDT-TTF(C10 173
4)2
B MICROWAVE CAVITY APPARATUS
1S6
REFERENCES
200
BIOGRAPHICAL SKETCH
214
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
ANISOTROPY IN THE INFRARED, OPTICAL
AND TRANSPORT PROPERTIES OF HIGH
TEMPERATURE SUPERCONDUCTORS
By
Manuel Alberto Quijada
April 1994
Chairman: David B. Tanner
Major Department: Physics
The optical properties of the high-temperature superconductors are extremely
unusual. We have extensively studied superconducting high-quality single crystals
of YBa2Cu307_5, Bi2Sr2CaCu208, and La2Cu04+^. All these materials have Cu02
planes as the entities responsible for the metallic behavior and superconductivity.
Polarized optical reflectance measurements were taken both above and below the
superconducting state on a wide frequency range.
All these materials display interesting anisotropy in their optical properties. In
I^CuO,^
particular, optical investigations of the oxygen-doped reveal the out-of-
plane (c axis) spectrum of this material is typical of an insulator with the optical
conductivity dominated by optical phonons. In contrast, the a6-plane optical spec-
trum is characterized by a metallic conductivity in the far infrared. We also find
evidence of electron-phonon interaction that is enhanced when the afr-plane optical
vii
response is measured on the face of the crystal that has the c axis parallel to the
propagation vector of the light.
The normal-state infrared conductivity of the Cu02 planes shows a strong,
nearly temperature-independent, broad band in the midinfrared in addition to a
strong temperature-dependent narrow Drude-like band in the far infrared. There
is also anisotropy in the infrared conductivities between the a and b axes of both
YBaoCusOy-j and I^Si^CaCmOs. In the case of YBaoCuaOy-^, the strong
anisotropy can be mostly attributed to the presence of CuO chains along the b axis.
One striking result is that in spite of the fact that BioS^CaCuoOs does not have
the CuO chains, we observed anisotropy between the a and b axes infrared conduc-
tivity of this compound as well. The presence of this anisotropy even in the super-
conducting state suggests two possibilities. One possibility could be an anisotropic
superconducting order parameter. A second explanation is that the overall conduc-
tivity is composed of a simple Drude term combined with a more broad midinfrared
component. The observed higher absorption in the low-frequency region along the
b axis could be explained by an anisotropic second midinfrared component in the
optical conductivity.
vm
CHAPTER
I
INTRODUCTION
The discovery of superconductivity in the copper oxides by Bednorz and Miiller
in 1986 has revolutionized the field of condensed matter physics. The importance of
this remarkable discovery can not be overstated. On the one hand, it offers promising
technological applications for materials that lose their resistance to the flow of electri-
cal current above liquid nitrogen temperatures. On the other hand, many experiments
have provided ample evidence of the exciting new phenomena present in these mate-
rials. Early measurements were designed to learn if the superconducting properties
of these materials could be explained in the context of the Bardeen-Cooper-Schrieffer
(DCS) theory for conventional superconductors. Some of those initial results sup-
ported a BCS-like theory. Among these, flux quantization3 and the AC Josephson
effect4 show that the elementary charge in the superconducting state is 2e rather than
e. In addition, photoemission5-7 and tunneling8,9 experiments suggest the presence
of a superconducting energy gap. At the same time, there has been an accumu-
lation of evidence for an unconventional nature of the high-T materials. Some of
c
the most important results that have emerged are high superconducting transition
temperature,1'10'11 linear dc resistivity in the normal state,12'13 and extremely small
coherence lengths. Perhaps the second most striking property in these materials,
'
16-21
beside their high-Tc value, is the anisotropy in their physical properties.
As soon as these materials were discovered, there began an intense effort to study
their optical properties.""""'1 Soon, it was realized that the strong anisotropy that
is observed in the electrical properties is continued in the infrared where the optical
properties are also very anisotropic. The study of this anisotropy by optical
means has provided some important results but at the same time has raised some
unresolved questions. As it is well known, superconductivity in these materials is
associated with the quasi-two dimensional CuC>2 planes. Most optical studies related
to the anisotropy in these materials have concentrated in the anisotropy between the
directions perpendicular to (c axis) and parallel to the Cu02 planes. Research of the
anisotropy within the C11O2 (ab) planes has been studied to a lesser degree. In view
of the orthorhombic distortion that exists in these planes there are two important
questions that must be addressed: (1) how this structural anisotropy affects the
anisotropy of the 2-d electronic structure in the normal state and (2) what if any is
the anisotropy of the superconducting order parameter?
Since the energy gap plays a central role in the BCS theory, substantial efforts
have been devoted to observing this gap by optical methods.30,31 One of the ad-
vantage of the optical methods compared to, for example, tunneling is that direct
electrical contact to the sample surface is not necessary. This is especially important
since crystals and films may have dead layers near the surface that make it nearly
impossible for current to tunnel between an electrode and the superconductor. In an
optical experiment, by contrast, the probing radiation can penetrate a few thousand
A
into the sample so the presence of dead layers becomes less of an issue. This tech-
nique, which has been used with great success in the past to study energy gaps in
conventional superconductors, has also given valuable information in solids about lat-
tice vibrations, electron-phonon coupling, low-lying excitations, and electronic band
structures. In the context of the BCS theory, the presence of a gap means that for
<
photon energies less than 2A, the bulk properties of the superconductor at T T
c
show only an inductive part, with the real or absorptive part being zero. So, in order
for there to be absorption in the material, the photon energy must be larger than
2A. Only at energies above 2A, it is possible to break up Cooper pairs to produce
