Table Of ContentSuperconductivity of Metals and Cuprates
Superconductivity of Metals and Cuprates
J R Waldram
Lecturer in Physics, Cavendish Laboratory
Co-Director, IRC in Superconductivity
Fellow, Pembroke College
University of Cambridge
Institute of Physics Publishing
Bristol and Philadelphia
© IOP Publishing Ltd 1996
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British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
ISBN 0 85274 335 1 hbk
ISBN 0 85274 337 8 pbk
Library of Congress Cátaloging-in-Publication Data
Waldram, J. R.
Superconductivity of metals and cuprates / J. R. Waldram.
p. cm.
Includes bibliographical references and index.
ISBN 0-85274-335-1 (alk. paper). - - ISBN 0-85274-337-8 (pbk: alk.
paper)
1. Superconductivity. I. Title.
QC611.92.W35 1996
537.6'23 - - dc20 96-19055
CIP
Published by Institute of Physics Publishing, wholly owned by The Institute of
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Printed in the UK by J W Arrowsmith Ltd, Bristol
This book is dedicated to
the Staff and Students of the
Royal Society Mond Laboratory
Cambridge
1933-1973
Contents
Preface xiii
1 Introduction 1
1.1 The aims of this book 1
1.2 The absence of electrical resistance 1
1.3 Thermal properties and the two-fluid model 3
1.4 Type I and type II superconductors 5
1.5 Other superconducting materials 6
1.6 The layout of this book 8
2 The superfluid 10
2.1 The two-fluid model in BCS theory 10
2.2 The supercurrent and the superfluid wavefunction 13
2.3 Introduction of the magnetic vector potential 15
2.4 The first London equation and perfect conductivity 17
2.5 The second London equation and perfect diamagnetism 18
2.6 The Meissner effect, flux trapping and flux quantization 21
2.7 Gauge transformations and the London gauge 24
2.8 Thermoelectric effects 26
2.9 The rotating superconductor 28
2.10 Other superfluid properties 30
3 The ideal phase transition 32
3.1 Field energy conventions 32
3.2 The thermodynamic critical field B 34
c
3.3 The critical field curve B(T) 35
C
3.4 Entropy and heat capacity 36
4 Ginzburg—Landau theory 39
4.1 The Landau theory of phase transitions 39
4.2 The Ginzburg-Landau free energy 43
4.3 The Ginzburg-Landau equations 44
viii Superconductivity
4.4 Penetration depth and coherence length 47
4.5 Microscopic expressions for the parameters 48
4.6 Dimensionless forms 49
4.7 Critical current density of a thin film 51
4.8 The Little-Parks effect 52
4.9 The NS boundary energy 54
4.10 The quantized flux line 56
4.11 Supercooling and the surface sheath 58
5 Superconducting states with internal magnetic flux 61
5.1 The macroscopic magnetization description 61
5.2 Samples with finite demagnetizing coefficient 63
5.3 The intermediate state of type I superconductors 65
5.4 The intermediate state in wires carrying currents 67
5.5 The mixed state of type II superconductors 70
5.6 The ideal mixed-state magnetization curve 73
5.7 Transport current and the H field in the mixed state 76
5.8 Driving force and dissipation in the mixed state 78
5.9 Pinning forces in the mixed state 80
5.10 Mixed-state critical current density as a function of B 84
5.11 Magnetization in the presence of flux pinning 86
5.12 Flux flow resistance 88
5.13 Hall and thermoelectric effects in the mixed state 89
6 Josephson effects 92
6.1 Weak links and the Josephson current-phase relation 92
6.2 Josephson effects in the voltage-source model 94
6.3 Josephson effects in the current-source model 96
6.4 Josephson inductance and the plasma resonance 100
6.5 The connection between Josephson phase and flux 101
6.6 Quantum interference between two weak links 103
6.7 Quantum interference within a single junction 105
6.8 Self-field effects in wide junctions 106
7 Groundwork of BCS theory 113
7.1 Picture of the attractive interaction 113
7.2 The attractive matrix element 115
7.3 The BCS ground state compared with the Fermi sea 118
7.4 The BCS ground state as a condensed pair state 119
7.5 Energetics of the BCS ground state 121
7.6 Pair excitations of the BCS state 124
7.7 Electron-like excitations of the BCS state 126
7.8 The BCS state at finite temperature 128
7.9 The weak-coupling limit 129
7.10 The isotope effect 131
Contents ix
8 BCS properties for weak coupling 134
8.1 Thermodynamic parameters 134
8.2 Further properties of the electron-like excitations 135
8.3 Scattering rates for electron-like excitations 136
8.4 Mean free path 139
8.5 Thermal conductivity 140
8.6 Acoustic attenuation 142
8.7 Effects visible in NMR 143
8.8 Tunnelling of normal excitations 146
8.9 Josephson operators in tunnelling theory 149
8.10 Theory of single-particle and Josephson tunnelling 150
9 The meaning of the order parameter 156
9.1 Off-diagonal long-range order for bosons 156
9.2 Occupation number and phase in the superfluid state 159
9.3 The pair function in BCS states 160
9.4 The amplitude of & and J in BCS theory 162
s
10 The non-local form of BCS theory 165
10.1 The Hamiltonian in terms of local operators 165
10.2 Electron-like excitations and the linear approximation 166
10.3 The local gap field and the Bogoliubov equations 168
10.4 The non-local equation for A(r) 169
10.5 The kernel in terms of thermal Green's functions 170
10.6 The BCS kernel 171
10.7 The dirty limit kernel 174
10.8 Ginzburg-Landau theory derived from non-local theory 176
10.9 Surface impedance and non-local electrodynamics 178
10.10 Size and T dependence of the penetration depth 181
10.11 Theory of the electromagnetic kernel 183
10.12 High-frequency conductivity and the two-fluid model 186
10.13 Summary of characteristic lengths 190
11 Further theory and properties 194
11.1 The proximity effect 194
11.2 Andréev reflection 198
11.3 Non-equilibrium states and relaxation times 202
11.4 Charge imbalance effects 204
11.5 Gap anisotropy 206
11.6 p- and d-wave superconductors 207
11.7 The effect of depairing interactions 209
11.8 The effect of scattering on the energy gap 212
11.9 Fermi-liquid theory and heavy-fermion superconductors 212
11.10 Theory of strong-coupling superconductors 215
11.11 Properties of strongly coupled superconductors 217
