Theory of superconductivity

349 Pages·1999·8.892 MB·English

by  Schrieffer, John Robert

Theory of
Superconductivity
Revised Printing

T h e o r y o f
S
u p e r c o n d u c t i v i t y
R evised P r in tin g
J.
R. ScHRIEFFER
Florida State University
Tallahassee, Florida
CRC Press
Taylor & Francis Group
Boca Raton London New York
CRC Press is an imprint of the
Taylor & Francis Group, an informa business
ABP
Advanced Book Program
The publisher is pleased to acknowledge the assistance of Paul Orban, who produced
the illustrations for the original edition. The revised edition (198.3) includes an
Appendix containing Nobel Lectures, December 11, 1972, by J. R. Schrieffer, Leon N.
Cooper, and John Bardeen, reprinted with permission of the Nobel Foundation.
Copyright © 1973 by the Nobel Foundation.
First published 1964 by Westview Press
Published 2018 by CRC Press
Taylor & Francis Group
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Boca Raton, FL 33487-2742
,
CRC Press is an imprint of the Taylor & Francis Group an informa business
Copyright © 1999, 1964 by J. R. Schrieffer
No claim to original U.S. Government works
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Library of Congress Catalog Card Number: 99^60035
ISBN 13: 978-0-7382-0120-7 (pbk)
Cover design by Suzanne Heiser
CONTENTS
Editor’s Foreword vii
Preface xv
Preface to the Revised Printing xvi i
I 1
Chapter introduction
1-1 Simple Experimental Facts 4
1-2 Phenomenological Theories 9
2 24
Chapter the pairing theory of superconductivity
2-1 Physical Nature of the Superconducting State 24
2-2 The One-Pair Problem 28
2-3 Landau’s Theory of a Fermi Liquid 34
2-4 The Pairing Approximation 36
2-5 Quasi-Particle Excitations 44
2-6 Linearized Equations of Motion 49
2-7 Concluding Remarks 57
ix
x Contents
3 61
Chapter applications of the pairing theory
3-1 Justification of the Pairing Hypothesis 61
3-2 Acoustic Attenuation Rate 62
3-3 Nuclear-Spin Relaxation Rate 69
3-4 Electromagnetic Absorption 72
3-5 Physical Origin of the Coherence Factors 74
3-6 Electron Tunneling 78
3-7 Other Applications of the Pairing Theory 87
4 89
Chapter electron- ion system
4-1 The Electron-ion Hamiltonian 89
4-2 Bare Phonons 92
4-3 Bare Electrons 95
4-4 Bare Electron-Phonon Interaction 98
4-5 The Electron-Phonon Hamiltonian 102
5
Chapter field-theoretic methods in the
103
MANY-BODY PROBLEM
5-1 The Schrodinger, Heisenberg, and
Interaction Pictures 103
5-2 The Green’s Function Approach 105
5-3 The Free Fermi Gas 108
5-4 Spectral Representation of (?(p, r) 112
5-5 Analytic Properties of 115
G
5-6 Physical Interpretation of 6r(p, 116
p0)
5-7 Interpretation of A(p, 119
co)
5-8 The One-Phonon Green’s Function 124
5-9 Perturbation Series 126
6 137
Chapter elementary excitations in normal metals
6-1 The Electron Gas with Coulomb Interactions 137
6-2 The Coupled Electron-Phonon System 148
Contents xi
Chapter 7 field-theoretic methods applied to
164
SUPERCONDUCTIVITY
7-1 Instability of the Normal Phase 164
7-2 Nambu-Gor’kov Formalism 169
7-3 Zero-Temperature Excitation Spectrum 180
7-4 Extension to Finite Temperature 193
Chapter 8 electromagnetic properties of
203
SUPERCONDUCTORS
8-1 London Rigidity 203
8-2 Weak-Field Response 206
8-3 The Meissner-Ochsenfeld Effect 212
8-4 Electromagnetic Properties for Finite q and 220
w
8-5 Gauge Invariance 224
8-6 The Vertex Function and Collective Modes 233
8-7 Flux Quantization 240
8-8 The Knight Shift 244
8-9 The Ginsburg-Landau-Gor’kov Theory 248
254
Conclusion
257
Appendix second quantization formalism
A-l Occupation-Number Representation 257
A-2 Second Quantization for Bosons 259
A-3 Second Quantization for Fermions 265
1972 267
Appendix Nobel Lectures,
Macroscopic Quantum Phenomena from Pairing
in Superconductors
J. R. Schrieffer 267
Microscopic Quantum Interference Effects in the
Theory of Superconductivity
Leon N. Cooper 279
Electron-Phonon Interactions and Superconductivity
John Bardeen 300
xii Contents
Notes and References 317
Index 329
t \ b / A 4 * c e J - Q o s o k Q , Im 4 * c 4
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