Quantum Theory of Conducting Matter (eBook)

Shigeji Fujita is Professor of Physics at State University of New York at Buffalo and has published 3 books with the Springer family since 1996.  His areas of expertise include statistical physics, solid and liquid state physics, superconductivity and Quantum Hall Effect theory.  Kei Ito is in the research division of the National Center for University Entrance Examinations in Tokyo, Japan.

Preface 5
Contents 8
Constants, Signs, Symbols, and GeneralRemarks 13
Contents of Book 1 19
1 Superconductors -- Introduction 22
Basic Properties of a Superconductor 22
Zero Resistance 22
Meissner Effect 22
Ring Supercurrent and Flux Quantization 24
Josephson Effects 25
Energy Gap 27
Sharp Phase Change 27
Occurrence of a Superconductor 28
Elemental Superconductors 28
Compound Superconductors 29
High-Tc Superconductors 30
Theoretical Survey 30
The Cause of Superconductivity 31
The Bardeen--Cooper--Schrieffer Theory 31
Quantum Statistical Theory 33
References 34
2 Electron--Phonon Interaction 35
Phonons and Lattice Dynamics 35
Electron--Phonon Interaction 39
Phonon--Exchange Attraction 43
References 47
3 The BCS Ground State 48
Introduction 48
The Reduced Hamiltonian 49
The BCS Ground State 51
Discussion 58
The Nature of the Reduced Hamiltonian 58
Bindeng Energy per Pairon 58
Critical Field Bc and Binding Energy |w0| 58
The Energy Gap 59
The Energy Gap Equations 59
Neutral Supercondensate 60
Cooper Pairs (Pairons) 60
Formation of a Supercondensate and Occurrenceof Superconductors 61
Blurred Fermi Surface 62
References 62
4 The Energy Gap Equations 63
Introduction 63
Energy-Eigenvalue Problem in Second Quantization 64
Energies of Quasi-Electrons at 0K 67
Derivation of the Cooper Equation 69
Energy Gap Equations at 0K 72
Temperature-Dependent Gap Equations 74
Discussion 77
Ground State 77
Supercondensate Density 77
Energy Gap (T) 77
Energy Gap Equations at 0 K 78
Energy Gap Equations Below Tc 78
References 78
5 Quantum Statistics of Composites 79
Ehrenfest--Oppenheimer--Bethe's Rule 79
Two-Particle Composites 80
Discussion 86
References 89
6 Quantum Statistical Theory 90
The Full Hamiltonian 90
The Cooper Pair Problem 92
Moving Pairons 94
The Bose--Einstein Condensation 96
The BEC in 3D, =cp 101
Discussion 103
References 105
7 Quantum Tunneling 106
Introduction 106
Quantum Tunneling in S--I--S Systems 107
Quantum Tunneling in S1--I--S2 114
Discussion 118
References 118
8 Compound Superconductors 119
Introduction 119
Type II Superconductors 119
Optical Phonons 124
Discussion 127
References 127
9 Supercurrents and Flux Quantization 128
Ring Supercurrent 128
Phase of the Quasi-Wavefunction 131
London's Equation: Penetration Depth 134
Quasi-Wavefunction and Its Evolution 138
Discussion 141
Supercurrents 141
Supercurrent is Not Hindered by Impurities 141
The Supercurrent Cannot Gain Energy from a DC Voltage 141
Critical Fields and Critical Currents 142
Supercurrent Ring and Flux Quantization 142
Meissner Effect and Surface Supercurrent 142
London's Equation 143
Penetration Depth 143
References 144
10 Ginzburg--Landau Theory 145
Introduction 145
Derivation of the GL Equation 147
Discussion 149
Penetration Depth 152
References 154
11 Josephson Effects 156
Josephson Tunneling and Interference 156
Equations Governing a Josephson Current 160
AC Josephson Effect and Shapiro Steps 163
Discussion 166
Josephson Tunneling 166
Interference and Analogy with Laser 166
GL Wavefunction, Quasi-Wavefunction, and Pairon Density Operator 166
Josephson--Feynman Equations 167
AC Josephson Effect and Shapiro Steps 167
Independent Pairon Picture 168
References 168
12 High Temperature Superconductors 169
Introduction 169
Layered Structures and 2-D Conduction 169
The Hamiltonian 172
The Ground State 175
High Critical Temperature 178
The Heat Capacity 180
Two Energy Gaps: Quantum Tunneling 180
Asymmetric I--V Curves for S--I--N 181
Scattered Data for Energy Gaps 182
Complicated I--V Curves 182
References 182
13 Doping Dependence of bold0mu mumu TTRawTTTTbold0mu mumu ccRawcccc 184
Introduction 184
Theory 184
Discussion 188
References 190
14 The Susceptibility in Cuprates 191
Introduction 191
Theory 194
Discussion 199
References 200
15 bold0mu mumu ddRawdddd-Wave Cooper Pair 202
Introduction 202
Phonon--Exchange Attraction 202
d-Wave Pairon Formalism 204
Discussion 205
References 205
16 Transport Properties Above bold0mu mumu TTRawTTTTbold0mu mumu ccRawcccc 206
Introduction 206
Simple Kinetic Theory 207
Resistivity 207
Hall Coefficient 210
Hall Angle 211
Data Analysis 211
Discussion 214
References 214
17 Other Theories 216
Gorter--Cassimir's Two Fluid Model 216
London--London's Theory 216
Ginzburg--Landau Theory 217
Electron--Phonon Interaction 218
The Cooper Pair 219
BCS Theory 219
Bose--Einstein Condensation 222
Josephson Theory 223
High Temperature Superconductors 224
Quantum Hall Effect 224
References 225
18 Summary and Remarks 228
Summary 228
Remarks 231
Thin Films 231
Nonmagnetic Impurities 232
Magnetic Impurities 232
Intermediate State 232
Critical Currents: Silsbee's Rule 232
Mixed State: Pinning Vortex Lines 233
Critical Currents in Type II Superconductors 233
Concluding Remarks 233
Reference 234
Appendix: Second Quantization 235
Boson Creation and Annihilation Operators 235
Observables 239
Fermion Creation and Annihilation Operators 241
Heisenberg Equation of Motion 242
Bibliography 246
Index 249