Electron Liquids

322 Pages·1998·9.54 MB·English

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

96 Springer Series in Solid-State Sciences
Edited by Manuel Cardona
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and A.V. Postnikov 116 Electron Spectrum of Gapless Semiconductors
99 Electronic Properties of High-Tc By J. M. Tsidilkovski
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102 Conjugated CoO(lucting Polymers
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120 Optical Properties of III-V Semiconductors
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Akira Isihara
Electron Liquids
With 116 Figures
Second Edition
Springer
Professor Akira Isihara, Ph. D.
JIDECO of Bardstone, Inc., 901 Withrow Court, Bardstown, KY 40004, USA
Series Editors:
Professor Dr., Ores. h. c. Manuel Cardona
Professor Dr., Ores. h. c. Peter Fulde*
Professor Dr., Ores. h. c. Klaus von Klitzing
Professor Dr., Ores. h. c. Hans-Joachim Queisser
Max-Planck-Institut fiir Festkorperforschung, Heisenbergstrasse I, D-70569 Stuttgart, Germany
* Max-Planck-Institut fiir Physik kornplexer Systerne, Bayreuther Strasse 40, Haus 16
D-01187 Dresden, Germany
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Library of Congress Cataloging-in-PubJication Data
Isihara, A. (Akira) Electron liquids 1 Akira Isihara. - 2nd ed. p. cm. - (Springer series in solid-state sciences; 96)
Includes bibliographical references and index. ISBN-13:978-3-642-80394-9 I. Solid state physics.
2. Electronic structure. 3. Electro-holw droplets. 4. Plasma (Ionized gases) I. Title. II. Series. QCl76.I75 1997
530.4'12-dc21 97-25655 CIP
ISSN 0171-1873
ISBN-13: 978-3-642-80394-9 e-ISBN-13: 978-3-642-80392-5
DOl: 10.1007/978-3-642-80392-5
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Preface
Several years have passed since the first edition of this book was published.
During this period, significant developments in the study of electron systems
have taken place, especially in the areas ofhigh-Tc superconductivity and the
quantized Hall effect. These developments, and such fascinating subjects as
crystallization and the stability of matter are included in the second edition.
Bardstown, KY A.Isiham
June 1997
Preface to the First Edition
The study of electronic properties reveals a common basis for a variety of sys
tems, including gaseous plasmas, ionic solutions, metals, and semiconductors.
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, impu
rities, and fields. Moreover, the recent discoveries of the quantum Hall effect,
high-Tc superconductors, and localization phenomena, along with the intr~
duction 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, comprehensive review
on electronic properties in such diverse areas and materials.
The title indicates emphasis on electron correlations. Chapter I starts with
an introductory description of electron systems, including classification, char
acterization, and models. It provides the reader with a general account of the
amazingly diverse electron systems. It is followed by discussions on strongly
coupled gaseous plasmas, electron-hole liquids, magnetic response, lowdimen
sional systems, heavy Fermions, high-Tc superconductivity, localization, the
quantum Hall effect, phase transition, and the stability of matter.
For simplicity the natural unit in which Ii. = 1 and 2m = 1 is used,
particularly for complicated expressions, m being the electron mass. However,
ordinary 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 vis
ited 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 Atsushi and Hikaru who gave him many constructive suggestions. He is
indebted to various investigators, physical societies, and publishers for per
mission to reproduce figures. These include the American Physical Society,
the Physical Society of Japan, Progress of Theoretical Physics, Nature, Phys-
VIII Preface to the First Edition
ica Status Solidi, Pergamon Press, Inc., North-Holland Publishing Company,
Plenum 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
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 Two-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. . . . . . . . . . . .. 17
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 ................................... 34
2.3 Plasmon Dispersion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 36
3. One-Component Plasmas at High Temperatures. . . . . . . . .. 41
r
3.1 e and Series. . . . . . . . . .. . . . . . . . . . . .. . . . . . . . .. . . .. . . . .. 41
3.2 Quantum Effects at High Temperatures. . . .. . . .. . . .. . . .. .. 47
3.3 Short-Distance Correlations. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 51
4. Low Temperature Plasmas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 55
4.1 Asymptotic Correlations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 55
4.1.1 Long-Distance Correlations and the Effect of Impurities 55
4.1.2 Ladder Diagram Contribution. . . . . . . . . . . . . . . . . . . . .. 57
4.2 Correlation Energy in Three Dimensions .................. 60
4.2.1 Ideal Gas Contribution.. . . .. . . . . . . . . . . .. . . . . . . . ... 61
4.2.2 First-Order Exchange Contribution. . . . . . . . . . . . . . . .. 61
4.2.3 Ring Diagram Contribution. . . . . . . . . . . . . . . . . . . . . . .. 62
4.2.4 Direct Calculation of the Ring Energy .............. 63
4.2.5 Second-Order Exchange Contribution. . . . . . . . . . . . . .. 64
X Contents
4.2.6 Correlation Energy. . . .. . . . . . . .. . . .. . . . .. . . . . . . ... 65
4.3 Correlation Energy of 2D Electrons. . . . . . . . . . . . . . . . . . . . . .. 66
5. Electron-Hole Liquids .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 71
5.1 Excitons.............................................. 71
5.2 Phase Diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 78
5.3 2D Electron-Hole Plasma ............................... 82
6. Correlation in a Magnetic Field. . . . . . . . . . . . . . . . . . . . . . . . . .. 89
6.1 Spatial Correlation in a Magnetic Field. . . . . . . . . . . . . . . . . . .. 89
6.2 Magnetic Response in Three Dimensions .................. 95
6.2.1 Exchange Effect at High Temperatures. . .. . . . . . . .. .. 95
6.2.2 Ideal Electron Gas at Low Temperatures .. . . . . . . . . .. 96
6.2.3 Exchange Effects at Low Temperatures. . . . . . . . . . . . .. 98
6.2.4 Correlation Effects ............................... 99
6.2.5 Local Field Correction ............................ 105
6.3 Effective g-Factor in Si Inversion Layers ................... 106
6.4 Coulomb Effects on 2D de Haas-van Alphen Oscillations .... 111
6.4.1 Chemical Potential ............................... 111
6.4.2 Exchange Effect .................................. 113
6.4.3 Correlation Contribution .......................... 115
6.4.4 de Haas-van Alphen Oscillations ................... 116
6.5 Field Induced SDW States of 1D Conductors .............. 120
7. Electronic Specific Heat .................................. 127
7.1 Correlation Effects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 127
7.1.1 Lidiard Approximation ............................ 127
7.1.2 Exchange and Correlation Effects ................... 129
7.1.3 Specific Heat of 2D Electrons ...................... 133
7.2 Magnetothermal Effect in Two Dimensions ................ 134
7.3 Heavy Fermions ........................................ 140
8. Magnetoconductivity in Two Dimensions ................. 149
8.1 Magnetoconductivity of 2D Electrons ..................... 149
8.2 Memory Function Formalism ............................. 156
8.3 Anomalous Cyclotron Resonance ......................... 161
9. Localization .............................................. 169
9.1 Anderson Localization and Scaling. . . . . . . . . . . . . . . . . . . . . . . . 169
9.2 Weak Localization ...................................... 173
9.2.1 Interference Effect ................................ 173
9.2.2 Magnetic Field Effects ............................ 177
9.3 Interaction Effect ....................................... 183
Contents XI
10. Hopping, Percolation and Conductance Fluctuations ...... 189
10.1 Hopping and Percolation ................................ 189
10.2 Universal Conductance Fluctuations in 1D Systems ......... 199
10.3 Conductance of TTF/ TCNQ ............................. 205
11. High-Tc Superconductivity ................................ 211
11.1 Electron Pairing in BCS Theory ................... , ...... 211
11.2 Properties of High-Tc Superconductors .................... 214
11.2.1 2-1-4 Compounds ................................ 214
11.2.2 1-2-3 Compounds ................................ 216
11.2.3 Copperless Oxides ................................ 218
11.2.4 Characteristic Properties .......................... 219
11.3 Theoretical Consideration ............................... 223
12. Integral Quantum Hall Effect ............................. 231
12.1 Quantization of Hall Conductivity of 2D Electrons .......... 231
12.2 Localization and Scaling ................................. 240
12.3 Theoretical Interpretation ............................... 244
13. Fractional Quantum Hall Effect ........................... 251
13.1 Experimental Results ................................... 251
13.2 Ground State of the FQHE .............................. 256
13.3 Elementary Excitations and Off-Diagonal Long Range Order. 262
14. Phase Transition and Stability of Matter ................. 269
14.1 Crystallization ......................................... 269
14.2 Properties of an Electron Lattice ......................... 271
14.3 Stability of Matter ...................................... 273
A. Appendix ................................................. 279
A.l Pair Distribution Function ............................... 279
A.2 Classical and Quantum Chains . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
A.3 Ring Diagram Formulas ................................. 291
A.4 Density Functional Approach ............................ 295
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299
Subject Index ........................ " ...................... 314