Electron Liquids

309 Pages·1993·9.92 MB·English

by  Professor Akira Isihara Ph. D. (auth.)

96
Springer Series in Solid-State Sciences
Edited by Manuel Cardona
Springer Series in Solid-State Sciences
Editors: M. Cardona P. Fulde K. von Klitzing H.-J. Queisser
Managing Editor: H. K.Y. Lotsch
Volumes 1-89 are listed at the end of the book
90 Earlier and Recent Aspects of Superconductivity Editors: J. G. Bednorz and K. A. Miiller
91 Electronic Properties of Conjugated Polymers III Basic Models and Applications
Editors: H. Kuzmany, M. Mehring, and S. Roth
92 Physics and Engineering Applications of Magnetism Editors: Y. Ishikawa and N. Miura
93 Quasicrystals Editors: T. Fujiwara and T. Ogawa
94 Electronic Conduction in Oxides By N. Tsuda, K. Nasu, A. Yanase, and K. Siratori
95 Electronic Materials A New Era in Materials Science
Editors: J. R. Chelikowsky and A. Franciosi
96 Electron Liquids By A. Isihara
97 Localization and Confinement of Electrons in Semiconductors
Editors: F. Kuchar, H. Heinrich, and G. Bauer
98 Magnetism and the Electronic Structure of Crystals
By V. A. Gubanov, A. I. Liechtenstein, and A.V. Postnikov
99 Electronic Properties of High-Tc Superconductors and Related Compounds
Editors: H. Kuzmany, M. Mehring, and J. Fink
100 Electron Correlations in Molecules and Solids By P. Fulde
101 High Magnetic Fields in Semiconductor Physics III
Quantum Hall Effect, Transport and Optics By G. Landwehr
102 Conjugated Conducting Polymers Editor: H. Kiess
103 Molecular Dynamics Simulations Editor: F. Yonezawa
104 Products of Random Matrices in Statistical Physics
By A. Crisanti, G. Paladin, and A. Vulpiani
105 Self-Trapped Excitons By K. S. Song and R. T. Williams
106 Physics of High-Temperature Superconductors Editors: S. Maekawa and M. Sato
107 Electronic Properties of Polymers Orientation and Dimensionality of Conjugated Systems
Editors: H. Kuzmany, M. Mehring, and S. Roth
108 Site Symmetry in Crystals Theory and Applications
By R. A. Evarestov and Y. P. Smirnov
109 Transport Phenomena in Mesoscopic Systems By H. Fukuyama, T. Ando
1 10 Symmetry and Optical Phenomena in Superlattices and Other Heterostructures
By E. L. Ivchenko, G. E. Pikus
III Low-Dimensional Electronic Systems New Concepts
By. G. Bauer, F. Kuchar, H. Heinrich
Akira Isihara
Electron Liquids
With 116 Figures
Springer-Verlag
Berlin Heidelberg New York
London Paris Tokyo
Hong Kong Barcelona
Budapest
Professor Akira Isihara, Ph. D.
JlDECO of Bardstown, Inc., 901 Withrow Court, Bardstown, KY 40004, USA
Series Editors:
Professor Dr., Dres. h. c. Manuel Cardona
Professor Dr., Dr. h. c. Peter Fulde
Professor Dr., Dr. h. c. Klaus von Klitzing
Professor Dr., Dres. h. c. Hans-Joachim Queisser
Max-Planck-Insitut flir Festkorperforschung, Heisenbergstrasse 1,
W -7000 Stuttgart 80, Fed. Rep. of Germany
Managing Editor:
Dr. Helmut K. V. Lotsch
Springer-Verlag, Tiergartenstrasse 17, W-6900 Heidelberg, Fed. Rep. of Germany
ISBN-I3: 978-3-642-97305-5 e-ISBN-13: 978-3-642-97303-1
DOl: 10.1007/978-3-642-97303-1
Library of Congress Cataloging-in-Publication Data. Isihara, A. (Akira). Electron liquids 1 Akira
Isihara. p. cm. - (Springer series in solid-state sciences; v. 96) Includes bibliographical references and
index.ISBN·ll 978-3-642-97305-5(Berlin: acid-free paper).ISBN-ll 978-3-M2-97305-5 (New York: acid-free
paper) 1. Solid state physics. 2. Electronic structure. 3. Electron-hole droplets. 4. Plasma (Ionized
gases) 1. Title. II. Series. QC176.l75 1993 530.4'12-dc20 92-20407
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© Springer-Verlag Berlin Heidelberg 1993
Softcover reprint of the hardcover 15t edition 1993
The use of general descriptive names, registered names, trademarks, etc. in this publication does not
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VI Preface
Press, Gordon & Breach Science Publishers, Inc., and lOP Publishing Ltd. The
author's original work in this book was supported by the National Science
Foundation and the Office of Naval Research.
Buffalo, NY A.Isihara
July 1992
Preface
The study of electronic properties reveals a common basis for a variety of
systems, including gaseous plasmas, ionic solutions, metals, and semiconduc
tors. This study started with one-electron properties in free space, as discussed
in solid-state books. However, significant progress has been made recently in
more realistic and complicated cases with interactions, confinements, im
purities, and fields. Moreover, the recent discoveries of the quantum Hall ef
fect, high-Tc superconductors, and localization phenomena, along with the in
troduction of low-dimensional materials have opened new areas and have led
to a tremendous number of articles in existing journals and even new
specialized journals. This book has been written to provide a new, comprehen
sive review on electronic properties in such diverse areas and materials.
The title indicates emphasis on electron correlations. Chapter 1 starts with
an introductory description of electron systems, including classification,
characterization, and models. It provides the reader with a general account of
the amazingly diverse electron systems. It is followed by discussions on strong
ly coupled gaseous plasmas, electron-hole liquids, magnetic response, low
dimensional systems, heavy Fermions, high-Tc superconductivity, localization,
and the quantum Hall effect.
For simplicity the natural unit in which h = 1 and 2m = 1 is used, par
ticularly for complicated expressions, m being the electron mass. However, or
dinary units are restored whenever desirable. This restoration can easily be
made by considering dimensions.
Each chapter has been written so as to be self-contained, so that the reader
can start at any chapter without going through previous chapters. Nevertheless,
an effort has been made to maintain uniformity and coherence as a single
book.
The author had an opportunity to meet with Professor Cardona who
visited Buffalo in the spring of 1989. The present book has emerged as a result
of his encouragement and stimulation. The patience and efforts of Dr. Lotsch
have also contributed to its completion. The author is especially grateful to At
sushi and Hikaru who gave him many constructive suggestions. He is indebted
to various investigators, physical societies, and publishers for permission to
reproduce figures. These include the American Physical Society, the Physical
Society of Japan, Progress of Theoretical Physics, Nature, Physica Status
Solidi, Pergamon Press, Inc., North-Holland Publishing Company, Plenum
Contents
1. General Description of Electron Systems . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Classification of Electron Systems ......................... 1
1.2 Low-Dimensional Electron Systems ........................ 5
1.2.1 1Wo-Dimensional Electron Systems ................... 5
1.2.2 One-Dimensional Electron Systems ................... 10
1.3 Characteristic Lengths ................................... 13
1.4 Fermi Liquid Theory .................................... 15
1.5 Tight Binding, Anderson and Hubbard Models ............. 18
2. Dielectric Function ......................................... 21
2.1 RPA Dielectric Function ................................. 21
2.2 Beyond the RPA ........................................ 27
2.2.1 Monte Carlo Calculations ........................... 27
2.2.2 Hubbard's Attempt... . ... . ....... .............. . ... 29
2.2.3 Phenomenological Consideration of e(q, w) ........... 30
2.2.4 Self-Consistent Approach ........................... 31
2.2.5 Excess Energy ..................................... 35
2.3 Plasmon Dispersion ..................................... 36
3. One-Component Plasmas at High Temperatures ................ 43
r
3.1 e and Series .......................................... 43
3.2 Quantum Effects at High Temperatures .................... 50
3.3 Short-Distance Correlations .............................. 54
4. Low Temperature Plasmas ................................... 57
4.1 Asymptotic Correlations ................................. 57
4.1.1 Long-Distance Correlations and the Effect
of Impurities ...................................... 57
4.1.2 Ladder Diagram Contribution ....................... 59
4.2 Correlation Energy in Three Dimensions ................... 62
4.2.1 Ideal Gas Contribution ............................. 63
4.2.2 First-Order Exchange Contribution ................... 64
4.2.3 Ring Diagram Contribution ......................... 64
4.2.4 Direct Calculation of the Ring Energy ................ 66
4.2.5 Second-Order Exchange Contribution . . . . . . . . . . . . . . . . . 67
4.2.6 Correlation Energy ................................. 68
4.3 Correlation Energy of 2D Electrons ....................... 69
VIII Contents
5. Electron - Hole Liquids ..................................... 73
5.1 Excitons ............................................. 73
5.2 Phase Diagram ....................................... 80
5.3 2D Electron-Hole Plasma ............................. 84
6. Correlation in a Magnetic Field ............................. 91
6.1 Spatial Correlation in a Magnetic Field .................. 91
6.2 Magnetic Response in Three Dimensions ................. 97
6.2.1 Exchange Effect at High Temperatures ............. 97
6.2.2 Ideal Electron Gas at Low Temperatures ........... 99
6.2.3 Exchange Effects at Low Temperatures ............. 100
6.2.4 Correlation Effects .............................. 102
6.2.5 Local Field Correction ........................... 108
6.3 Effective g-Factor in Si Inversion Layers ................. 109
6.4 Coulomb Effects on 2D de Haas-van Alphen Oscillations. 114
6.4.1 Chemical Potential .............................. 114
6.4.2 Exchange Effect ................................ 116
6.4.3 Correlation Contribution . . . . . . . . . . . . . . . . . . . . . . . . . 118
6.4.4 de Haas-van Alphen Oscillations ................. 119
6.5 Field Induced SDW States of ID Conductors. . . . . . . . . . . . . 123
7. Electronic Specific Heat .................................... 129
7.1 Correlation Effects .................................... 129
7.1.1 Lidiard Approximation .......................... 129
7.1.2 Exchange and Correlation Effects ................. 131
7.1.3 Specific Heat of 2D Electrons .................... 135
7.2 Magnetothermal Effect in Two Dimensions ............... 137
7.3 Heavy Fermions ...................................... 142
8. Magnetoconductivity in 1\vo Dimensions ..................... 151
8.1 Magnetoconductivityof 2D Electrons. . . . . . . . . . . . . . . . . . . . 151
8.2 Memory Function Formalism ........................... 159
8.3 Anomalous Cyclotron Resonance ....................... 163
9. Localization .............................................. 171
9.1 Anderson Localization and Scaling ...................... 171
9.2 Weak Localization .................................... 176
9.2.1 Interference Effect .............................. 176
9.2.2 Magnetic Field Effects ........................... 180
9.3 Interaction Effect ..................................... 185
10. Hopping, Percolation and Conductance Fluctuations ........... 193
10.1 Hopping and Percolation .............................. 193
10.2 Universal Conductance Fluctuations in 1D Systems ........ 203
10.3 Conductance of TTF/TCNQ ........................... 210
Contents IX
11. High TcSupercouductivity .................................. 215
11.1 Electron Pairing in BCS Theory ........................ 215
11.2 Properties of High Tc Superconductors .................. 218
11.2.1 2-1-4 Compounds ............................... 218
11.2.2 1-2-3 Compounds ............................... 220
11.2.3 Copperless Oxides .............................. 222
11.2.4 Characteristic Properties ......................... 223
11.3 Theoretical Consideration .............................. 227
12. Integral Quantum Hall Effect ............................... 233
12.1 Quantization of Hall Conductivity of 2D Electrons ....... 233
12.2 Localization and Scaling ............................... 242
12.3 Theoretical Interpretation .............................. 246
13. Fractional Quantum Hall Effect ............................. 253
13.1 Experimental Results .................................. 253
13.2 Ground State of the FQHE ............................ 258
13.3 Elementary Excitations
and Off-Diagonal Long Range Order .................... 264
Appendix .................................................... 271
A.1 Pair Distribution Function ............................. 271
A.2 Classical and Quantum Chains ......................... 277
A.3 Ring Diagram Formulas ............................... 284
A.4 Density Functional Approach ........................... 287
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 291
Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 303
A high-purity germanium crystal is cut into a 4 mm disk and stressed at the top by a nylon screw.
The sample is immersed in liquid helium at 2 K and excited from the far side by an argon-ion laser.
The electrons and holes produced by photoexcitation condense into electron-hole droplets and are
drawn into the region beneath the screw, where the energy gap is lowered by a local strain. The
droplets coalesce into a single large drop at the strain maximum, or energy maximum. Bright emis
sion from the drop is produced by the radiative recombination of electrons and holes at about
1.75!lm wavelength, which is detected with an infrared vidicon tube. [J.P. Wolfe, W.L. Hansen,
E. E. Haller, R. S. Markiewicz, C. Kittel, C. D. Jeffries: Phys. Rev. Lett. 34, 1292 (1975)]