Superconductivity (eBook)

Front Cover 1
Superconductivity 4
Copyright Page 5
Table of Contents 6
Preface 14
Chapter 1. Properties of the Normal State 18
I. Introduction 18
II. Conduction Electron Transport 18
III. Chemical Potential and Screening 21
IV. Electrical Conductivity 22
V. Frequency Dependent Electrical Conductivity 23
VI. Electron–Phonon Interaction 24
VII. Resistivity 24
VIII. Thermal Conductivity 25
IX. Fermi Surface 25
X. Energy Gap and Effective Mass 27
XI. Electronic Specific Heat 28
XII. Phonon Specific Heat 29
XIII. Electromagnetic Fields 31
XIV. Boundary Conditions 32
XV. Magnetic Susceptibility 33
XVI. Hall Effect 35
Further Reading 37
Problems 37
Chapter 2. The Phenomenon of Superconductivity 38
I. Introduction 38
II. A Brief History 38
III. Resistivity 40
IV. Zero Resistance 50
V. Transition Temperature 52
VI. Perfect Diamagnetism 55
VII. Fields inside a Superconductor 58
VIII. Shielding Current 59
IX. Hole in Superconductor 61
X. Perfect Conductivity 64
XI. Transport Current 65
XII. Critical Field and Current 66
XIII. Temperature Dependences 68
XIV. Concentration of Super Electrons 70
XV. Critical Magnetic Field Slope 70
XVI. Critical Surface 71
Further Reading 74
Problems 74
Chapter 3. The Classical Superconductors 76
I. Introduction 76
II. Elements 77
III. Physical Properties of Superconducting Elements 80
IV. Compounds 83
V. Alloys 83
VI. Miedema's Empirical Rules for Alloys 88
VII. Compounds with the NaCl Structure 90
VIII. Type A15 Compounds 91
IX. Laves Phases 94
X. Chevrel Phases 95
XI. Heavy Electron Systems 97
XII. Charge-Transfer Organics 101
XIII. Chalcogenides and Oxides 103
XIV. Barium Lead–Bismuth Oxide Perovskite 104
XV. Barium-Potassium Bismuth-Oxide Cubic Perovskite 104
XVI. Buckminsterfullerenes 104
XVII. Borocarbides 105
Further Reading 106
Problems 106
Chapter 4. Thermodynamic Properties 108
I. Introduction 108
II. Specific Heat above Tc 109
III. Discontinuity at Tc 113
IV. Specific Heat below Tc 114
V. Density of States and Debye Temperature 115
VI. Thermodynamic Variables 116
VII. Thermodynamics of a Normal Conductor 117
VIII. Thermodynamics of a Superconductor 118
IX. Superconductor in Zero Field 122
X. Superconductor in a Magnetic Field 123
XI. Normalized Thermodynamic Equations 128
XII. Specific Heat in a Magnetic Field 129
XIII. Evaluating the Specific Heat 131
XIV. Order of the Transition 133
XV. Thermodynamic Conventions 134
XVI. Concluding Remarks 134
Further Reading 135
Problems 135
Chapter 5. Ginzburg–Landau Theory 138
I. Introduction 138
II. Order Parameter 139
III. Ginzburg–Landau Equations 140
IV. Zero-Field Case Deep inside Superconductor 141
V. Zero-Field Case near Superconductor Boundary 143
VI. Fluxoid Quantization 144
VII. Penetration Depth 145
VIII. Critical Current Density 149
IX. London Equations 150
X. Exponential Penetration 150
XI. Normalized Ginzburg-Landau Equations 154
XII. Type I and Type II Superconductivity 156
XIII. Upper Critical Field Bc2 157
XIV. Quantum Vortex 159
Further Reading 163
Problems 164
Chapter 6. BCS Theory 166
I. Introduction 166
II. Cooper Pairs 167
III. BCS Order Parameter 169
IV. Generalized BCS Theory 171
V. Singlet Pairing in a Homogeneous Superconductor 177
VI. Self-Consistent Equation for the Energy Gap 180
VII. Response of a Superconductor to a Magnetic Field 185
Further Reading 188
Chapter 7. Perovskite and Cuprate Crystallographic Structures 190
I. Introduction 190
II. Perovskites 191
III. Cubic Barium Potassium Bismuth Oxide 195
IV. Barium Lead Bismuth Oxide 196
V. Perovskite-Type Superconducting Structures 196
VI. Aligned YBa2Cu3O7 199
VII. Body Centering 204
VIII. Body-Centered La2CuO4 and Nd2CuO4 205
IX. Body-Centered BiSrCaCuO and TIBaCaCuO 211
X. Aligned HgBaCaCuO 215
XI. Buckminsterfullerenes 218
XII. Symmetries 220
XIII. Crystal Chemistry 221
XIV. Comparison with Classical Superconductor Structures 223
XV. Conclusions 223
Further Reading 224
Problems 224
Chapter 8. Hubbard Models and Band Structure 226
I. Introduction 226
II. Reciprocal Space and Brillouin Zone 227
III. Free Electron Bands in Two Dimensions 228
IV. Nearly Free Electron Bands 231
V. Fermi Surface in Two Dimensions 232
VI. Electron Configurations 234
VII. Hubbard Models 239
VIII. Transition Metal Elements 251
IX. A15 Compounds 251
X. Buckminsterfullerenes 253
XI. BaPb1_xBixO3 System 254
XII. Ba1_xKxBiO3 System 255
XIII. Band Structure of YBa2Cu3O7 256
XIV. Band Structure of (La1_xSrx)2CuO4 260
XV. Bismuth and Thallium Compounds 266
XVI. Mercury Compounds 267
XVII. Fermi Liquids 272
XVIII. Fermi Surface Nesting 273
XIX. Charge-Density Waves, Spin- Density Waves, and Spin Bags 273
XX. Mott-Insulator Transition 274
XXI. Anderson Interlayer Tunneling Scheme 275
XXII. Comparison with Experiment 276
XXIII. Discussion 278
Further Reading 280
Problems 280
Chapter 9. Type II Superconductivity 282
I. Introduction 282
II. Internal and Critical Fields 283
III. Vortices 290
IV. Vortex Anisotropies 299
V. Individual Vortex Motion 308
VI. Flux Motion 316
VII. Fluctuations 322
VIII. Quantized Flux 325
Further Reading 327
Problems 327
Chapter 10. Magnetic Properties 330
I. Introduction 330
II. Susceptibility 331
III. Magnetization and Magnetic Moment 331
IV. Magnetization Hysteresis 333
V. Zero Field Cooling and Field Cooling 334
VI. Granular Samples and Porosity 337
VII. Magnetization Anisotropy 338
VIII. Measurement Techniques 339
IX. Comparing Susceptibility and Resistivity Results 340
X. Ellipsoids in Magnetic Fields 341
XI. Demagnetization Factors 342
XII. Measured Susceptibilities 343
XIII. Sphere in a Magnetic Field 344
XIV. Cylinder in a Magnetic Field 346
XV. ac Susceptibility 348
XVI. Temperature-Dependent Magnetism 350
XVII. Pauli Limit and Upper Critical Fields 354
XVIII. Ideal Type II Superconductor 356
XIX. Magnets 358
Further Reading 358
Problems 359
Chapter 11. Intermediate and Mixed States 360
I. Introduction 360
II. Intermediate State 361
III. Surface Fields and Intermediate- State Configuration 361
IV. Type I Ellipsoid 363
V. Susceptibility 365
VI. Gibbs Free Energy for the Intermediate State 365
VII. Boundary-Wall Energy and Domains 367
VIII. Thin Film in Applied Field 369
IX. Domains in Thin Films 371
X. Current-Induced Intermediate State 374
XI. Mixed State in Type II Superconductors 379
Further Reading 379
Problems 379
Chapter 12. Critical States 382
I. Introduction 382
II. Current–Field Relations 383
III. Critical-State Models 385
IV. Fixed Pinning Model 386
V. Bean Model 388
VI. Reversed Critical States and Hysteresis 395
VII. Kim Model 410
VIII. Comparison of Critical-State Models with Experiment 414
IX. Concluding Remarks 416
Further Reading 417
Problems 417
Chapter 13. Tunneling 418
I. Introduction 418
II. The Phenomenon of Tunneling 418
III. Energy Level Schemes 420
IV. Tunneling Processes 421
V. Quantitative Treatment of Tunneling 425
VI. Tunneling Measurements 435
VII. Josephson Effect 443
VIII. Magnetic Field and Size Effects 454
Further Reading 469
Problems 469
Chapter 14. Transport Properties 472
I. Introduction 472
II. Inductive Superconducting Circuits 472
III. Current Density Equilibration 476
IV. Critical Current 478
V. Magnetoresistance 481
VI. Hall Effect 487
VII. Thermal Conductivity 490
VIII. Thermoelectric and Thermomagnetic Effects 496
IX. Photoconductivity 507
X. Transport Entropy 510
Further Reading 510
Problems 510
Chapter 15. Spectroscopic Properties 512
I. Introduction 512
II. Vibrational Spectroscopy 513
III. Optical Spectroscopy 524
IV. Photoemission 527
V. X-ray Absorption Edges 535
VI. Inelastic Neutron Scattering 541
VII. Positron Annihilation 545
VIII. Magnetic Resonance 546
Further Reading 563
Problems 563
References 566
Appendix 608
Index 618