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Theory of High Temperature Superconductivity : Fundamental Theories of Physics - Shigeji Fujita

Theory of High Temperature Superconductivity

Fundamental Theories of Physics

Hardcover Published: 31st December 2001
ISBN: 9781402001499
Number Of Pages: 374

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Flux quantization experiments indicate that the carriers, Cooper pairs (pairons), in the supercurrent have charge magnitude 2e, and that they move independently. Josephson interference in a Superconducting Quantum Int- ference Device (SQUID) shows that the centers of masses (CM) of pairons move as bosons with a linear dispersion relation. Based on this evidence we develop a theory of superconductivity in conventional and mate- als from a unified point of view. Following Bardeen, Cooper and Schrieffer (BCS) we regard the phonon exchange attraction as the cause of superc- ductivity. For cuprate superconductors, however, we take account of both optical- and acoustic-phonon exchange. BCS started with a Hamiltonian containing "electron" and "hole" kinetic energies and a pairing interaction with the phonon variables eliminated. These "electrons" and "holes" were introduced formally in terms of a free-electron model, which we consider unsatisfactory. We define "electrons" and "holes" in terms of the cur- tures of the Fermi surface. "Electrons" (1) and "holes" (2) are different and so they are assigned with different effective masses: Blatt, Schafroth and Butler proposed to explain superconductivity in terms of a Bose-Einstein Condensation (BEC) of electron pairs, each having mass M and a size. The system of free massive bosons, having a quadratic dispersion relation: and moving in three dimensions (3D) undergoes a BEC transition at where is the pair density.

Introduction
Basic Properties of a Superconductorp. 1
Occurrence of a Superconductorp. 8
Theoretical Backgroundp. 10
Elements of Kinetic Theoryp. 14
Superconducting Transitions
Three Phase Transitionsp. 19
Pairons Move as Massless Particlesp. 21
The Bose-Einstein Condensationp. 23
Bloch Electrons
Bloch Theoremp. 27
Fermi Liquid Modelp. 30
The Fermi Surfacep. 32
Heat Capacity; The Density of Statesp. 37
Equations of Motion for a Bloch Electronp. 39
Phonon Exchange Attraction
Phonons and Lattice Dynamicsp. 45
Electron-Phonon Interactionp. 49
Phonon-Exchange Attractionp. 54
Quantum Statistical Theory
Theory of Superconductivityp. 59
The Bardeen-Cooper-Schrieffer Theoryp. 61
Remarksp. 63
Cooper Pairs (Pairons)
The Cooper Problemp. 65
Moving Paironsp. 67
Energy-Eigenvalue Problem for a Quasiparticlep. 70
Derivation of the Cooper Equationp. 73
Superconductors at 0 K
The Generalized BCS Hamiltonianp. 77
The Ground-Statep. 82
Discussionp. 88
Quantum Statistics of Composites
Ehrenfest-Oppenheimer-Bethe's Rulep. 95
Two-Particle Compositesp. 96
Discussionp. 102
Bose-Einstein Condensation
Free Massless Bosons Moving in 2Dp. 107
Free Massless Bosons in 3Dp. 111
B-E Condensation of the Paironsp. 114
Discussionp. 115
The Energy Gap Equations
Introductionp. 123
Energies of Quasi-electrons at 0 Kp. 124
Energy Gap Equations at 0 Kp. 126
Temperature-Dependent Gap Equationsp. 128
Discussionp. 130
Pairon Energy Gaps and Heat Capacity
The Full Hamiltonianp. 133
Pairons Energy Gapsp. 135
Density of Condensed Paironsp. 138
Heat Capacityp. 141
Discussionp. 143
Quantum Tunneling
Introductionp. 147
Quantum Tunneling in S-I-S Systemsp. 148
Quantum Tunneling in S[subscript 1]-I-S[subscript 2]p. 156
Discussionp. 161
Flux Quantization
Ring Supercurrentp. 163
Phase of a Quasi-Wavefunctionp. 167
London's Equation. Penetration Depthp. 170
Quasi-Wavefunction and its Evolutionp. 175
Discussionp. 177
Ginzburg-Landau Theory
Introductionp. 181
Derivation of the G-L Equationp. 183
Condensation Energyp. 185
Penetration Depthp. 189
Josephson Effects
Josephson Effects and Supercurrent Interferencep. 193
Equations Governing a Josephson Currentp. 197
ac Josephson Effect and Shapiro Stepsp. 200
Discussionp. 204
Compound Superconductors
Introductionp. 207
Type II Superconductorsp. 208
Optical Phononsp. 213
Discussionp. 216
Lattice Structures of Cuprates
Introductionp. 217
Layered Structures and 2-D Conductionp. 217
Selected Cuprate Superconductorsp. 221
High-T[subscript c] Superconductors Below T[subscript c]
The Hamiltonianp. 227
The Ground Statep. 231
High Critical Temperaturep. 233
The Heat Capacityp. 235
Two Energy Gaps; Quantum Tunnelingp. 236
Doping Dependence of T[subscript c]
Introductionp. 241
Critical Temperature T[subscript c]p. 242
Doping Dependence of T[subscript c]p. 245
Transport Properties Above T[subscript c]
Introductionp. 249
Simple Kinetic Theoryp. 250
Data Analysisp. 255
Discussionp. 257
Out-of-Plane Transport
Introductionp. 259
Theoryp. 260
Data Analysisp. 265
Discussionp. 266
Seebeck Coefficient (Thermopower)
Introductionp. 269
Theoryp. 272
Discussionp. 275
Seebeck Coefficients in Metalsp. 277
In-Plane Seebeck Coefficient S[subscript ab]p. 279
Out-of-Plane Seebeck Coefficient S[subscript c]p. 280
Discussionp. 283
Magnetic Susceptibility
Introductionp. 285
Theoryp. 287
Discussionp. 292
Infrared Hall Effect
Introductionp. 295
Theory and Experiments for Aup. 298
Theory for YBa[subscript 2]Cu[subscript 3]O[subscript 7]p. 302
Data Analysis and Discussionp. 303
d-Wave Cooper Pairs
Introductionp. 307
Phonon-Exchange Attractionp. 307
d-Wave pairon Formationp. 309
Discussionp. 310
Connections with Other Theories
Gorter-Cassimir's Two Fluid Modelp. 311
London-London's Theoryp. 312
Ginzburg-Landau Theoryp. 313
Electron-Phonon Interactionp. 314
The Cooper Pairp. 315
BCS Theoryp. 315
Bose-Eintein Condensationp. 318
Josephson Theoryp. 319
High Temperature Superconductorsp. 320
Quantum Hall Effectp. 321
Summary and Remarks
Summaryp. 325
Remarksp. 329
A Second Quantization
Referencesp. 345
Bibliographyp. 355
Indexp. 359
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9781402001499
ISBN-10: 1402001495
Series: Fundamental Theories of Physics
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 374
Published: 31st December 2001
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.5 x 15.5  x 2.54
Weight (kg): 1.64