Superconductivity (eBook)

Front Cover 1
Superconductivity 4
Copyright Page 5
Table of Contents 8
Preface to the First Edition 18
Preface to the Second Edition 22
Chapter 1 Properties of the Normal State 26
I. Introduction 26
II. Conduction Electron Transport 26
III. Chemical Potential and Screening 29
IV. Electrical Conductivity 30
V. Frequency Dependent Electrical Conductivity 31
VI. Electron–Phonon Interaction 32
VII. Resistivity 32
VIII. Thermal Conductivity 33
IX. Fermi Surface 33
X. Energy Gap and Effective Mass 35
XI. Electronic Specific Heat 36
XII. Phonon Specific Heat 37
XIII. Electromagnetic Fields 39
XIV. Boundary Conditions 40
XV. Magnetic Susceptibility 41
XVI. Hall Effect 43
Further Reading 45
Problems 45
Chapter 2 Phenomenon of Superconductivity 48
I. Introduction 48
II. Brief History 49
III. Resistivity 52
A. Resistivity above Tc 52
B. Resistivity Anisotropy 53
C. Anisotropy Determination 56
D. Sheet Resistance of Films: Resistance Quantum 57
IV. Zero Resistance 59
A. Resistivity Drop at Tc 59
B. Persistent Currents below Tc 60
V. Transition Temperature 61
VI. Perfect Diamagnetism 65
VII. Magnetic Fields Inside a Superconductor 68
VIII. Shielding Current 69
IX. Hole in Superconductor 70
X. Perfect Conductivity 73
XI. Transport Current 74
XII. Critical Field and Current 77
XIII. Temperature Dependences 77
XIV. Two Fluid Model 79
XV. Critical Magnetic Field Slope 80
XVI. Critical Surface 80
Further Reading 83
Problems 83
Chapter 3 Classical Superconductors 86
I. Introduction 86
II. Elements 86
III. Physical Properties of Superconducting Elements 89
IV. Compounds 92
V. Alloys 96
VI. Miedema’s Empirical Rules 97
VII. Compounds with the NaCl Structure 100
VIII. Type A15 Compounds 101
IX. Laves Phases 103
X. Chevrel Phases 105
XI. Chalcogenides and Oxides 107
Problems 107
Chapter 4 Thermodynamic Properties 108
I. Introduction 108
II. Specific Heat above TC 109
III. Discontinuity at TC 114
IV. Specific Heat below TC 115
V. Density of States and Debye Temperature 115
VI. Thermodynamic Variables 116
VII. Thermodynamics of a Normal Conductor 117
VIII. Thermodynamics of a Superconductor 120
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 130
XIII. Further Discussion of the Specific Heat 132
XIV. Order of the Transition 134
XV. Thermodynamic Conventions 134
XVI. Concluding Remarks 135
Problems 135
Chapter 5 Magnetic Properties 138
I. Introduction 138
II. Susceptibility 139
III. Magnetization and Magnetic Moment 139
IV. Magnetization Hysteresis 141
V. Zero Field Cooling and Field Cooling 142
VI. Granular Samples and Porosity 145
VII. Magnetization Anisotropy 146
VIII. Measurement Techniques 147
IX. Comparison of Susceptibility and Resistivity Results 149
X. Ellipsoids in Magnetic Fields 149
XI. Demagnetization Factors 150
XII. Measured Susceptibilities 152
XIII. Sphere in a Magnetic Field 153
XIV. Cylinder in a Magnetic Field 154
XV. ac Susceptibility 156
XVI. Temperature-Dependent Magnetization 159
A. Pauli Paramagnetism 159
B. Paramagnetism 159
C. Antiferromagnetism 161
XVII. Pauli Limit and Upper Critical Field 162
XVIII. Ideal Type II Superconductor 164
XIX. Magnets 166
Problems 167
Chapter 6 Ginzburg–Landau Theory 168
I. Introduction 168
II. Order Parameter 169
III. Ginzburg–Landau Equations 170
IV. Zero-Field Case Deep Inside Superconductor 171
V. Zero-Field Case near Superconductor Boundary 173
VI. Fluxoid Quantization 174
VII. Penetration Depth 175
VIII. Critical Current Density 179
IX. London Equations 180
X. Exponential Penetration 180
XI. Normalized Ginzburg–Landau Equations 185
XII. Type I and Type II Superconductivity 186
XIII. Upper Critical Field BC2 187
XIV. Structure of a Vortex 189
A. Differential Equations 189
B. Solutions for Short Distances 190
C. Solution for Large Distances 191
Further Reading 193
Problems 194
Chapter 7 BCS Theory 196
Introduction 196
II. Cooper Pairs 197
III. The BCS Order Parameter 199
IV. The BCS Hamiltonian 201
V. The Bogoliubov Transformation 202
VI. The Self-Consistent Gap Equation 203
A. Solution of the Gap Equation Near Tc 204
B. Solution At T = 0 204
C. Nodes of the Order Parameter 204
D. Single Band Singlet Pairing 205
E. S-Wave Pairing 205
F. Zero-Temperature Gap 207
G. D-Wave Order Parameter 209
H. Multi-Band Singlet Pairing 210
VII. Response of a Superconductor to a Magnetic Field 213
Appendix A. Derivation of the Gap Equation Near Tc 215
Further Reading 217
Chapter 8 Cuprate Crystallographic Structures 220
I. Introduction 220
II. Perovskites 221
A. Cubic Form 221
B. Tetragonal Form 223
C. Orthorhombic Form 223
D. Planar Representation 224
III. Perovskite-Type Superconducting Structures 225
IV. Aligned YBa2Cu3O7 227
A. Copper Oxide Planes 229
B. Copper Coordination 229
C. Stacking Rules 230
D. Crystallographic Phases 230
E. Charge Distribution 231
F. YBaCuO Formula 232
G. YBa2Cu4O8 and Y2Ba4Cu7O15 232
V. Aligned HgBaCaCuO 233
VI. Body Centering 235
VII. Body-Centered La2CuO4, Nd2CuO4 and Sr2RuO4 236
A. Unit Cell of La2CuO4 Compound (T Phase) 236
B. Layering Scheme 237
C. Charge Distribution 237
D. Superconducting Structures 238
E. Nd2CuO4 Compound (T' Phase) 238
F. La2–x–yRxSryCuO4 Compounds (T* Phase) 241
G. Sr2RuO4 Compound (T Phase) 242
VIII. Body-Centered BiSrCaCuO and TlBaCaCuO 243
A. Layering Scheme 243
B. Nomenclature 244
C. Bi-Sr Compounds 245
D. Tl-Ba Compounds 245
E. Modulated Structures 246
F. Aligned TI-Ba Compounds 247
G. Lead Doping 247
IX. Symmetries 247
X. Layered Structure of the Cuprates 248
XI. Infinite-Layer Phases 250
XII. Conclusions 252
Further Reading 252
Problems 253
Chapter 9 Unconventional Superconductors 256
I. Introduction 256
II. Heavy Electron Systems 256
III. Magnesium Diboride 261
A. Structure 261
B. Physical Properties 262
C. Anisotropies 262
D. Fermi Surfaces 264
E. Energy Gaps 266
IV. Borocarbides and Boronitrides 268
A. Crystal Structure 268
B. Correlations of Superconducting Properties with Structure Parameters 269
C. Density of States 270
D. Thermodynamic and Electronic Properties 272
E. Magnetic Interactions 274
F. Magnetism of HoNi2B2C 279
V. Perovskites 281
A. Barium-Potassium-Bismuth Cubic Perovskite 281
B. Magnesium-Carbon-Nickel Cubic Perovskite 282
C. Barium-Lead-Bismuth Lower Symmetry Perovskite 283
VI. Charge-Transfer Organics 284
VII. Buckminsterfullerenes 285
VIII. Symmetry of the Order Parameter in Unconventional Superconductors 287
A. Symmetry of the Order Parameter in Cuprates 287
a. Hole-doped high-Tc cuprates 287
b. Electron-doped cuprates 288
B. Organic Superconductors 289
C. Influence of Bandstructure on Superconductivity 291
a. MgB2 291
b. NbSe2 292
c. CaAlSi 293
D. Some Other Superconductors 293
a. Heavy-fermion superconductors 293
b. Borocarbides 294
c. Sr2RuO4 294
d. MgCNi3 295
IX. Magnetic Superconductors 295
A. Coexistence of superconductivity and magnetism 295
B. Antiferromagnetic Superconductors 297
C. Magnetic Cuprate Superconductor – SmCeCuO 297
Chapter 10 Hubbard Models and Band Structure 300
I. Introduction 300
II. Electron Configurations 301
A. Configurations and Orbitals 301
B. Tight-Binding Approximation 302
III. Hubbard Model 306
A. Wannier Functions and Electron Operators 306
B. One-State Hubbard Model 307
C. Electron-Hole Symmetry 308
D. Half-Filling and Antiferromagnetic Correlations 309
E. t-J Model 310
F. Resonant-Valence Bonds 311
G. Spinons, Holons, Slave Bosons, Anyons, and Semions 312
H. Three-State Hubbard Model 312
I. Energy Bands 313
J. Metal-Insulator Transition 314
IV. Band Structure of YBa2Cu3O7 315
A. Energy Bands and Density of States 316
B. Fermi Surface: Plane and Chain Bands 317
V. Band Structure of Mercury Cuprates 318
VI. Band Structures of Lanthanum, Bismuth, and Thallium Cuprates 324
A. Orbital States 324
B. Energy Bands and Density of States 324
VII. Fermi Liquids 327
VIII. Fermi Surface Nesting 328
IX. Charge-Density Waves, Spin-Density Waves, and Spin Bags 328
X. Mott-Insulator Transition 329
XI. Discussion 330
Further Reading 330
Problems 330
Chapter 11 Type I Superconductivity and the Intermediate State 332
I. Introduction 332
II. Intermediate State 333
III. Surface Fields and Intermediate-State Configurations 333
IV. Type I Ellipsoid 335
V. Susceptibility 336
VI. Gibbs Free Energy for the Intermediate State 338
VII. Boundary-Wall Energy and Domains 340
VIII. Thin Film in Applied Field 342
IX. Domains in Thin Films 343
X. Current-Induced Intermediate State 347
XI. Recent Developments in Type I Superconductivity 351
A. History and General Remarks 351
B. The Intermediate State 354
C. Magneto-Optics with In-Plane Magnetization – a Tool to Study Flux Patterns 355
D. AC Response in the Intermediate State of Type I Superconductors 357
XII. Mixed State in Type II Superconductors 358
Problems 359
Chapter 12 Type II Superconductivity 362
I. Introduction 362
II. Internal and Critical Fields 363
A. Magnetic Field Penetration 363
B. Ginzburg-Landau Parameter 365
C. Critical Fields 367
III. Vortices 370
A. Magnetic Fields 371
B. High-Kappa Approximation 372
C. Average Internal Field and Vortex Separation 374
D. Vortices near Lower Critical Field 375
E. Vortices near Upper Critical Field 377
F. Contour Plots of Field and Current Density 377
G. Closed Vortices 379
IV. Vortex Anisotropies 380
A. Critical Fields and Characteristic Lengths 381
B. Core Region and Current Flow 382
C. Critical Fields 382
D. High-Kappa Approximation 386
E. Pancake Vortices 388
F. Oblique Alignment 388
V. Individual Vortex Motion 389
A. Vortex Repulsion 389
B. Pinning 392
C. Equation of Motion 393
D. Onset of Motion 394
E. Magnus Force 394
F. Steady-State Motion 395
G. Intrinsic Pinning 396
H. Vortex Entanglement 396
VI. Flux Motion 396
A. Flux Continuum 396
B. Entry and Exit 397
C. Two-Dimensional Fluid 397
D. Dimensionality 398
E. Solid and Glass Phases 399
F. Flux in Motion 399
G. Transport Current in a Magnetic Field 400
H. Dissipation 401
I. Magnetic Phase Diagram 402
VII. Fluctuations 403
A. Thermal Fluctuations 403
B. Characteristic Length 403
C. Entanglement of Flux Lines 404
D. Irreversibility Line 404
E. Kosterlitz–Thouless Transition 406
Problems 406
Chapter 13 Irreversible Properties 410
I. Introduction 410
II. Critical States 410
III. Current–Field Relationships 411
A. Transport and Shielding Current 411
B. Maxwell Curl Equation and Pinning Force 412
C. Determination of Current–Field Relationships 413
IV. Critical-State Models 413
A. Requirements of a Critical-State Model 413
B. Model Characteristics 413
V. Bean Model 414
A. Low-Field Case 414
B. High-Field Case 415
C. Transport Current 417
D. Combining Screening and Transport Current 418
E. Pinning Strength 420
F. Current-Magnetic Moment Conversion Formulae 421
a. Elliptical cross-section 421
b. Rectangular cross-section 421
c. Triangular cross-section 421
d. General remarks 422
VI. Reversed Critical States and Hysteresis 422
A. Reversing Field 423
B. Magnetization 426
C. Hysteresis Loops 426
D. Magnetization Current 428
VII. Perfect Type-I Superconductor 430
VIII. Concluding Remarks 431
Problems 431
Chapter 14 Magnetic Penetration Depth 434
I. Isotropic London Electrodynamics 434
II. Penetration Depth in Anisotropic Samples 436
III. Experimental Methods 438
IV. Absolute Value of the Penetration Depth 439
V. Penetration Depth and the Superconducting Gap 441
A. Semiclassical Model for Superfluid Density 441
a. Isotropic Fermi Surface 442
b. Anisotroic Fermi Surface, Isotropic gap function 443
B. Superconducting Gap 443
C. Mixed Gaps 444
D. Low-Temperatures 445
a. s-wave pairing 445
b. d-wave pairing 445
c. p-wave pairing 445
VI. Effect of Disorder and Impurities on the Penetration Depth 446
A. Non-Magnetic Impurities 446
B. Magnetic Impurities 447
VII. Surface Andreev Bound States 448
VIII. Nonlocal Electrodynamics of Nodal Superconductors 450
IX. Nonlinear Meissner Effect 451
X. AC Penetration Depth in the Mixed State (Small Amplitude Linear Response) 453
XI. The Proximity Effect and its Identification by Using AC Penetration Depth Measurements 455
Chapter 15 Energy Gap and Tunneling 458
I. Introduction 458
II. Phenomenon of Tunneling 458
A. Conduction-Electron Energies 459
B. Types of Tunneling 460
III. Energy Level Schemes 460
A. Semiconductor Representation 460
B. Boson Condensation Representation 461
IV. Tunneling Processes 461
A. Conditions for Tunneling 461
B. Normal Metal Tunneling 463
C. Normal Metal – Superconductor Tunneling 463
D. Superconductor – Superconductor Tunneling 464
V. Quantitative Treatment of Tunneling 465
A. Distribution Function 465
B. Density of States 467
C. Tunneling Current 467
D. N–I–N Tunneling Current 469
E. N–I–S Tunneling Current 469
F. S–I–S Tunneling Current 470
G. Nonequilibrium Quasiparticle Tunneling 472
H. Tunneling in unconventional superconductors 474
a. Introduction 474
b. Zero-Bias Conductance Peak 475
c. c-Axis Tunneling 476
VI. Tunneling Measurements 476
A. Weak Links 477
B. Experimental Arrangements for Measuring Tunneling 477
C. N–I–S Tunneling Measurements 479
D. S–I–S Tunneling Measurements 479
E. Energy Gap 480
F. Proximity Effect 482
G. Even–Odd Electron Effect 484
VII. Josephson Effect 484
A. Cooper Pair Tunneling 485
B. dc Josephson Effect 485
C. ac Josephson Effect 487
D. Driven Junctions 488
E. Inverse ac Josephson Effect 491
F. Analogues of Josephson Junctions 494
VIII. Magnetic Field and Size Effects 497
A. Short Josephson Junction 497
B. Long Josephson Junction 501
C. Josephson Penetration Depth 503
D. Two-Junction Loop 504
E. Self-Induced Flux 505
F. Junction Loop of Finite Size 507
G. Ultrasmall Josephson Junction 507
H. Arrays and Models for Granular Superconductors 510
I. Superconducting Quantum Interference Device 510
Problems 511
Chapter 16 Transport Properties 514
I. Introduction 514
II. Inductive Superconducting Circuits 514
A. Parallel Inductances 515
B. Inductors 515
C. Alternating Current Impedance 516
III. Current Density Equilibration 517
IV. Critical Current 520
A. Anisotropy 520
B. Magnetic Field Dependence 521
V. Magnetoresistance 522
A. Fields Applied above Tc 523
B. Fields Applied below Tc 525
C. Fluctuation Conductivity 526
D. Flux-Flow Effects 527
VI. Hall Effect 529
A. Hall Effect above Tc 530
B. Hall Effect below Tc 532
VII. Thermal Conductivity 533
A. Heat and Entropy Transport 533
B. Thermal Conductivity in the Normal State 534
C. Thermal Conductivity below Tc 536
D. Magnetic Field Effects 538
E. Anisotropy 538
VIII. Thermoelectric and Thermomagnetic Effects 538
A. Thermal Flux of Vortices 540
B. Seebeck Effect 541
C. Nernst Effect 543
D. Peltier Effect 547
E. Ettingshausen Effect 547
F. Righi–Leduc Effect 549
IX. Photoconductivity 549
X. Transport Entropy 552
Problems 553
Chapter 17 Spectroscopic Properties 556
I. Introduction 556
II. Vibrational Spectroscopy 557
A. Vibrational Transitions 557
B. Normal Modes 558
C. Soft Modes 558
D. Infrared and Raman Active Modes 558
E. Kramers-Kronig Analysis 560
F. Infrared Spectra 561
G. Light-Beam Polarization 563
H. Raman Spectra 564
I. Energy Gap 566
III. Optical Spectroscopy 568
IV. Photoemission 570
A. Measurement Technique 570
B. Energy Levels 571
C. Core-Level Spectra 576
D. Valence Band Spectra 577
E. Energy Bands and Density of States 579
V. X-Ray Absorption Edges 580
A. X-ray Absorption 580
B. Electron-Energy Loss 583
VI. Inelastic Neutron Scattering 584
VII. Positron Annihilation 586
VIII. Magnetic Resonance 590
A. Nuclear Magnetic Resonance 591
B. Quadrupole Resonance 596
C. Electron-Spin Resonance 599
D. Nonresonant Microwave Absorption 600
E. Microwave Energy Gap 602
F. Muon-Spin Relaxation 603
G. Mössbauer Resonance 604
Problems 606
References 608
Index 658