Theory of Nonequilibrium Superconductivity
by Kopnin, NikolaiFormat: Paperback
Pub. Date: 2009-07-15
Publisher(s): Oxford University Press
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Summary
This text is on the modern theory of superconductivity, It deals with the behavior of superconductors in external fields varying in time, and with transport phenomena in superconductors. The book starts with the fundamentals of the first-principle, microscopy theory of superconductivity, and guides the reader through the modern theoretical analysis directly to applications of the theory to practical problems. The reader of this book will learn about the methods of quantum field theory applied to nonstationary superconductivity in their most advanced formulation, namely about the so-called semi-classical version of the real-time Green's function technique applied to the celebrated Barbeen, Cooper, and Schrieffer model of superconductivity. A considerable part of the book is devoted to vortex dynamics, dealing with the behavior of superconductors in the most practical situation when they carry electric currents in the presence of a magnetic field.
Author Biography
Nikolai Kopnin works at the Helsinki University of Technology, and at L.D. Landau Institute for Theoretical Physics, Moscow.
Table of Contents
| Green Functions in the BCS Theory | |
| Introduction | p. 3 |
| Superconducting variables | p. 3 |
| Ginzburg-Landau theory | p. 4 |
| Example: Vortices in type II superconductors | p. 8 |
| Bogoliubov-de Gennes equations | p. 15 |
| Quasiclassical approximation | p. 16 |
| Nonstationary phenomena | p. 18 |
| Time-dependent Ginzburg-Landau theory | p. 18 |
| Microscopic argumentation | p. 21 |
| Boltzmann kinetic equation | p. 23 |
| Outline of the contents | p. 25 |
| Green functions | p. 27 |
| Second quantization | p. 27 |
| Schröet;dinger and Heisenberg operators | p. 29 |
| Imaginary-time Green function | p. 30 |
| Definitions | p. 30 |
| Example: Free particles | p. 34 |
| The Wick theorem | p. 36 |
| The real-time Green functions | p. 38 |
| Definitions | p. 38 |
| Analytical properties | p. 39 |
| The BCS model | p. 42 |
| BCS theory and Gor'kov equations | p. 42 |
| Magnetic field | p. 47 |
| Frequency and momentum representation | p. 48 |
| Order parameter of a d-wave superconductor | p. 52 |
| Derivation of the Bogoliubov-de Gennes equations | p. 53 |
| Thermodynamic potential | p. 55 |
| Example: Homogeneous state | p. 57 |
| Green functions | p. 57 |
| Gap equation for an s-wave superconductor | p. 58 |
| Perturbation theory | p. 60 |
| Diagram technique | p. 60 |
| Electric current | p. 61 |
| Superconducting alloys | p. 64 |
| Averaging over impurity positions | p. 64 |
| Magnetic impurities | p. 70 |
| Homogeneous state of an s-wave superconductor | p. 71 |
| Quasiclassical Method | |
| General Principles of the quasiclassical approximation | p. 77 |
| Quasiclassical Green functions | p. 77 |
| Density, current, and order parameter | p. 81 |
| Homogeneous state | p. 84 |
| Real-frequency representation | p. 86 |
| Example: Homogeneous state | p. 86 |
| Eilenberger equations | p. 88 |
| Self-energy | p. 90 |
| Normalization | p. 92 |
| Dirty limit. Usadel equations | p. 94 |
| Boundary conditions | p. 96 |
| Diffusive surface | p. 96 |
| Quasiclassical methods in stationary problems | p. 101 |
| s-wave superconductors with impurities | p. 101 |
| Small currents in a uniform state | p. 101 |
| Ginzburg-Landau theory | p. 103 |
| The upper critical field in a dirty alloy | p. 107 |
| Gapless s-wave superconductivity | p. 109 |
| Critical temperature | p. 110 |
| Gap in the energy spectrum | p. 111 |
| Aspects of d-wave superconductivity | p. 113 |
| Impurities and d-wave superconductivity | p. 113 |
| Impurity-induced gapless excitations | p. 114 |
| The Ginzburg-Landau equations | p. 115 |
| Bound states in vortex cores | p. 117 |
| Superconductors with s-wave pairing | p. 118 |
| d-wave superconductors | p. 122 |
| Quasiclassical method for layered superconductors | p. 125 |
| Quasiclassical Green functions | p. 125 |
| Eilenberger equations for layered systems | p. 128 |
| Lawrence-Doniach model | p. 129 |
| Order parameter | p. 130 |
| Free energy and the supercurrent | p. 132 |
| Microscopic derivation of the supercurrent | p. 134 |
| Applications of the Lawrence-Doniach model | p. 135 |
| Upper critical field | p. 136 |
| Intrinsic pinning | p. 137 |
| Nonequilibrium Superconductivity | |
| Nonstationary theory | p. 143 |
| The method of analytical continuation | p. 143 |
| Clean superconductors | p. 145 |
| Impurities | p. 149 |
| Order parameter, current, and particle density | p. 152 |
| The phonon model | p. 152 |
| Self-energy | p. 152 |
| Order parameter | p. 157 |
| Particle-particle collisions | p. 159 |
| Transport-like equations and the conservation laws | p. 161 |
| The Keldysh diagram technique | p. 163 |
| Definitions of the Keldysh functions | p. 163 |
| Dyson equation | p. 167 |
| Keldysh functions in the BCS theory | p. 168 |
| Quasiclassical method for nonstationary phenomena | p. 170 |
| Eliashberg equations | p. 170 |
| Self-energies | p. 172 |
| Order parameter, current, and particle density | p. 174 |
| Normalization of the quasiclassical functions | p. 174 |
| Generalized distribution function | p. 175 |
| s-wave superconductors with a short mean free path | p. 177 |
| Stimulated superconductivity | p. 181 |
| Kinetic equations | p. 186 |
| Gauge-invariant Green functions | p. 186 |
| Equations of motion for the invariant functions | p. 188 |
| Quasiclassical kinetic equations | p. 192 |
| Superconductors in electromagnetic fields | p. 194 |
| Discussion | p. 197 |
| Observables in the gauge-invariant representation | p. 199 |
| The electron density and charge neutrality | p. 201 |
| Collision integrals | p. 203 |
| Impurities | p. 204 |
| Electron-phonon collision integral | p. 205 |
| Electron-electron collision integral | p. 207 |
| Kinetic equations for dirty s-wave superconductors | p. 209 |
| Small gradients without magnetic impurities | p. 210 |
| Heat conduction | p. 211 |
| The time-dependent Ginzburg-Landau theory | p. 213 |
| Gapless superconductors with magnetic impurities | p. 213 |
| Generalized TDGL equations | p. 215 |
| TDGL theory for d-wave superconductors | p. 221 |
| d.c. electric field in superconductors. Charge imbalance | p. 226 |
| Vortex Dynamics | |
| Time-dependent Ginzburg-Landau analysis | p. 231 |
| Introduction | p. 231 |
| Energy balance | p. 233 |
| Moving vortex | p. 234 |
| Force balance | p. 236 |
| Flux flow | p. 238 |
| Single vortex: Low fields | p. 238 |
| Dense lattice: High fields | p. 240 |
| Direction of the vortex motion | p. 242 |
| Anisotropic superconductors | p. 243 |
| Low fields | p. 245 |
| High fields | p. 246 |
| Flux flow in layered superconductors | p. 246 |
| Motion of pancake vortices | p. 247 |
| Intrinsic pinning | p. 247 |
| Flux flow within a generalized TDGL theory | p. 248 |
| Dirty superconductors | p. 248 |
| d-wave superconductors | p. 251 |
| Discussion: Flux flow conductivity | p. 252 |
| Flux flow Hall effect | p. 253 |
| Modified TDGL equations | p. 254 |
| Hall effect: Low fields | p. 255 |
| High fields | p. 256 |
| Discussion: Hall effect | p. 256 |
| Vortex dynamics in dirty superconductors | p. 259 |
| Microscopic derivation of the force on moving vortices | p. 259 |
| Variation of the thermodynamic potential | p. 259 |
| Force on vortices | p. 260 |
| Diffusion controlled flux flow | p. 263 |
| Discussion | p. 269 |
| Vortex dynamics in clean superconductors | p. 271 |
| Introduction | p. 271 |
| Boltzmann kinetic equation approach | p. 272 |
| Forces in s-wave superconductors | p. 274 |
| Spectral representation for the Green functions | p. 277 |
| Useful identities | p. 279 |
| Distribution function | p. 282 |
| Localized excitations | p. 282 |
| Delocalized excitations | p. 287 |
| Flux flow conductivity | p. 290 |
| Discussion | p. 292 |
| Conductivity: Low temperatures | p. 292 |
| Conductivity: Arbitrary temperatures | p. 293 |
| Forces | p. 298 |
| Boltzmann kinetic equation | p. 303 |
| Canonical equations | p. 303 |
| Uniform order parameter | p. 303 |
| Boltzmann equation in presence of vortices | p. 306 |
| Quasiparticles in the vortex core | p. 307 |
| Transformation into the Boltzmann equation | p. 307 |
| Vortex mass | p. 311 |
| Equation of vortex dynamics | p. 312 |
| Vortex momentum | p. 314 |
| Vortex dynamics in d-wave superconductors | p. 315 |
| Distribution function | p. 315 |
| Conductivity | p. 318 |
| References | p. 320 |
| Index | p. 325 |
| Table of Contents provided by Ingram. All Rights Reserved. |
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