Volume I. Superconductivity: Conventional and Unconventional
Superconductors
List of Contributors ........................................... XV
1 History of Superconductivity: Conventional,
High-Transition Temperature and Novel Superconductors
K.H. Bennemann and J.B. Ketterson ........................... 3
1.1 Introduction .......................................... 3
1.2 Novel Superconductors ................................. 9
1.3 Granular Superconductors, Mesoscopic Systems,
Josephson Junctions .................................. 18
1.4 Outlook .............................................. 23
References ................................................. 25
2 Phenomenology and Microscopic Theory: Theoretical
Foundations
L. Pitaevskii .............................................. 27
2.1 Off-Diagonal Long-Range Order and Superfluidity ...... 27
2.2 Off-Diagonal Long-Range Order in Superconductors ..... 31
2.3 The London Equation .................................. 33
2.4 Thermodynamics of Superconductors in a Magnetic
Field ................................................ 35
2.5 The Intermediate State of Superconductors ............ 37
2.6 The Ginzburg-Landau Theory ........................... 38
2.7 Surface Energy at the Boundary Between Normal and
Superconducting Phases ............................... 42
2.8 Superconductors of the Second Kind ................... 45
2.9 Quantized Vortex Lines ............................... 46
2.10 Vortex-Vortex Interactions ........................... 49
2.11 Cooper Pairing ....................................... 52
2.12 Energy Spectrum of a Superconductor .................. 54
2.13 Thermodynamic Properties of Superconductors .......... 57
2.14 Elements of the Theory of Green's Functions .......... 62
2.15 Green's Function of a Superconductor ................. 65
2.16 Temperature Green's Functions ........................ 68
2.17 Temperature Green's Functions for a Superconductor ... 70
References ................................................. 71
3 Electron-Phonon Superconductivity
R. Marsiglio and J.P. Carbotte ............................. 73
3.1 Introduction ......................................... 74
3.2 The Electron-Phonon Interaction: Overview ............ 74
3.3 The Phonons .......................................... 92
3.4 The Critical Temperature and the Energy Gap ......... 108
3.5 Thermodynamics and Critical Magnetic Fields ......... 118
3.6 Response Functions .................................. 122
3.7 Anisotropy and MgB2 ................................. 139
3.8 Summary ............................................. 145
Appendix .................................................. 148
References ................................................ 153
4 Coexistence of Singlet Superconductivity and Magnetic
Order in Bulk Magnetic Superconductors and SF
Heterostructures
M.L. Kulic and A.I. Buzdin ................................ 163
4.1 Introduction ........................................ 164
4.2 Ferromagnetic Superconductors ....................... 169
4.3 Antiferromagnetic Superconductors (AFS) ............. 180
4.4 Magnetic Superconductors in the Magnetic Field ...... 183
4.5 Josephson Effect with Bulk Magnetic
Superconductors ..................................... 188
4.6 Superconductor/Ferromagnet Heterostructures ......... 189
4.7 Conclusion .......................................... 196
Appendix .................................................. 197
References ................................................ 199
5 Theory of Superconducting Alloys
I.P. Gor'kov .............................................. 201
5.1 Introduction ........................................ 201
5.2 Averages of Green Functions Over Impurities ......... 202
5.3 Superconducting Alloys with a Small Gap ............. 208
5.4 Paramagnetic Alloys and Gapless Superconductivity ... 216
5.5 Eilenberger Equations ............................... 218
5.6 Final Remark ........................................ 223
References ................................................ 224
6 Impurity Nanostructures and Quantum Interference in
Superconductors
D.K. Morr ................................................. 225
6.1 Introduction ........................................ 225
6.2 Review: Single Impurity Effects in Conventional
and Unconventional Superconductors .................. 228
6.3 Formalism ........................................... 231
6.4 Quantum Interference and Quantum Imaging in s-wave
Superconductors ..................................... 234
6.5 Quantum Interference Phenomena in dx2-y2-wave
Superconductors ..................................... 244
6.6 Molecules on the Surface of dx2-y2-wave
Superconductors ..................................... 250
6.7 Conclusions ......................................... 253
References ................................................ 256
7 Nanostructured Superconductors
G. Deutscher .............................................. 259
7.1 Introduction ........................................ 259
7.2 Nano-structured Compounds ........................... 260
7.3 The Granular Structure .............................. 260
7.4 Normal State Transport .............................. 262
7.5 Single Grain Behavior ............................... 265
7.6 Weakly Coupled Grains: Granular Insulators and
Super-Insulators .................................... 269
7.7 Well Coupled Grains ................................. 272
7.8 Critical Temperature of Granular Superconductors .... 275
References ................................................ 277
8 Proximity-Coupled Systems: Quasiclassical Theory of
Superconductivity
V. Chandrasekhar .......................................... 279
8.1 Introduction ........................................ 279
8.2 Transport Equations in the Diffusive
Approximation ....................................... 280
8.3 The Keldysh Green's Functions ....................... 283
8.4 The Quasiclassical Approximation .................... 288
8.5 Non-equilibrium Green's Functions for
Superconducting Systems ............................. 291
8.6 Quasiclassical Superconducting Green's Functions .... 294
8.7 The Dirty Limit: The Usadel Equation ................ 297
8.8 Parametrization of the Quasiclassical Green's
Function ............................................ 302
8.9 Applications of the Quasiclassical Equations to
Proximity-Coupled Systems ........................... 304
8.10 Summary ............................................. 311
References ................................................ 312
9 Principles of Josephson-Junction-Based Quantum
Computation
S.E. Shafranjuk and J.B. Ketterson ........................ 315
9.1 Introduction ........................................ 316
9.2 Josephson-Junction-Based Qubit Devices .............. 319
9.3 Qubit Dynamics ...................................... 329
9.4 Quantum Oscillations in Two Coupled Charge Qubits ... 345
9.5 SISIS Two-Qubit Gate with Intrinsic Coupling ........ 350
9.6 Conclusions ......................................... 361
Appendix .................................................. 362
References ................................................ 365
10 Fluctuation Phenomena in Superconductors
A.I. Larkin and A.A. Varlamov ............................. 369
10.1 Introduction ........................................ 370
10.2 Ginzburg-Landau Formalism: Thermodynamics ........... 373
10.3 Fluctuations Below the Critical Temperature ......... 390
10.4 Ginzburg-Landau Theory of Fluctuations in
Transport Phenomena ................................. 396
10.5 Fluctuations Near the S-I Transition ................ 405
10.6 Microscopic Derivation of the Time-Dependent
Ginzburg-Landau Equation ............................ 410
10.7 Microscopic Theory of Fluctuation Conductivity of
Layered Superconductors ............................. 416
10.8 Manifestation of Fluctuations in Various
Properties .......................................... 429
10.9 Conclusions ......................................... 452
References ................................................ 453
11 Universal Properties of Cuprate Superconductors:
Evidence and Implications
T. Schneider .............................................. 459
11.1 Introduction ........................................ 459
11.2 Critical Behavior at Finite Temperature ............. 465
11.3 Quantum Critical Behavior and Crossover Phenomena ... 471
11.4 Thin Films .......................................... 487
11.5 Concluding Remarks and Comparison with Other
Layered Superconductors ............................. 487
References ................................................ 489
12 Vortex Matter
G. Blatter and V.B. Geshkenbein ........................... 495
12.1 Introduction ........................................ 496
12.2 Ginzburg-Landau and London Theories ................. 502
12.3 Vortex Lines ........................................ 505
12.4 Vortex Lattice ...................................... 512
12.5 Layered Materials ................................... 518
12.6 Anisotropic Scaling Theory .......................... 532
12.7 Statistical Mechanics ............................... 538
12.8 Quenched Disorder: Pinning and Creep ................ 566
12.9 Uncorrelated Disorder: Collective Pinning and
Creep ............................................... 575
12.10 Correlated Disorder ................................. 605
12.11 Surface and Geometrical Barriers .................... 610
12.12 Vortex Glasses ...................................... 615
12.13 Concluding Remarks .................................. 621
References ................................................ 625
13 Unconventional Superconductivity in Novel Materials
M.B. Maple, E.D. Bauer, V.S. Zapf, and J. Wosnitza ........ 639
13.1 Introduction ........................................ 640
13.2 Conventional Superconductors Containing Localized
Magnetic Moments .................................... 641
13.3 ƒ-Electron Heavy Fermion Superconductors ............ 659
13.4 Organic Superconductors ............................. 696
13.5 Layered Cuprate and Ruthenate Superconductors ....... 717
13.6 Comparison of the Properties of Different Classes
of Novel Superconductors ............................ 741
References ................................................ 744
Volume II. Superconductivity: Novel Superconductors
List of Contributors ........................................... XV
14 High-Tc Superconductivity
H.R. Ott .................................................. 765
14.1 Introduction ........................................ 765
14.2 Typical Structural Characteristics .................. 767
14.3 Occurrence of Superconductivity ..................... 774
14.4 Physical Properties of Copper Oxides ................ 778
14.5 Physical Properties of Non-Cuprate High-Tc
Superconductors ..................................... 813
14.6 Final Remarks ....................................... 823
References ................................................ 823
15 Tunneling Spectroscopy of Conventional and
Unconventional Superconductors
J. Zasadzinski ............................................ 833
15.1 Introduction ........................................ 833
15.2 Basic Tunneling Phenomenology ....................... 835
15.3 Tunneling and Strong-Coupling Effects:
Microscopic Picture ................................. 841
15.4 Tunneling Spectroscopy of Conventional
Superconductors ..................................... 844
15.5 Tunneling in High-Temperature Superconductors ....... 847
15.6 Heavy Fermion Superconductors ....................... 861
15.7 Organic Superconductors ............................. 862
15.8 Other Materials ..................................... 863
15.9 Conclusions ......................................... 864
References ................................................ 865
16 Phase-Sensitive Tests of Pairing Symmetry in Cuprate
Superconductors
С.С. Tsuei and J.R. Kirtley ............................... 869
16.1 Introduction ........................................ 869
16.2 Phase Sensitive Tests: Theoretical Background ....... 874
16.3 Phase-Sensitive Tests: Experiments .................. 880
16.4 Angle-Resolved Determination of Gap Anisotropy in
YBCO ................................................ 901
16.5 Universality of the d-Wave Pair State ............... 902
16.6 Implications of d-Wave Pairing Symmetry ............. 907
16.7 Conclusions ......................................... 912
References ................................................ 913
17 Photoemission in the High-Tc Superconductors
J.C. Campuzano, M.R. Norman, and M. Randeria .............. 923
17.1 Introduction ........................................ 924
17.2 Basics of Angle-Resolved Photoemission .............. 924
17.3 The Valence Band .................................... 933
17.4 Normal State Dispersion and the Fermi Surface ....... 935
17.5 Superconducting Energy Gap .......................... 948
17.6 Pseudogap ........................................... 954
17.7 Photoemission Lineshapes and the Electron Self-
Energy .............................................. 963
17.8 Summary ............................................. 987
References ................................................ 988
18 Neutron Scattering and the Magnetic Response of
Superconductors and Related Compounds
S.M. Hayden ............................................... 993
18.1 Introduction ........................................ 993
18.2 The Neutron Scattering Technique .................... 994
18.3 The Static Spin Susceptibility of
Superconductors ..................................... 999
18.4 Magnetic Excitations in Metals and Weakly Coupled
Superconductors .................................... 1001
18.5 Excitations and Superconductive Pairing ............ 1003
18.6 High Temperature Superconductivity ................. 1004
18.7 Discussion ......................................... 1023
18.8 Final Remarks ...................................... 1024
References ............................................... 1024
19 Heavy-Fermion Superconductivity
P.S. Riseborough, G.M. Schmiedeshoff, and J.L. Smith ..... 1031
19.1 Overview ........................................... 1031
19.2 Introduction ....................................... 1033
19.3 Properties of the Normal State ..................... 1069
19.4 Properties of the Superconducting State ............ 1103
19.5 Heavy Fermion Superconducting Compounds ............ 1132
19.6 The Conclusion ..................................... 1140
References ............................................... 1141
20 Organic Superconductors
M. Lang and J. Müller .................................... 1155
20.1 Introduction ....................................... 1155
20.2 Characteristics of Organic Charge-Transfer
Conductors ......................................... 1157
20.3 Normal-State Properties ............................ 1162
20.4 Superconducting-State Properties ................... 1182
20.5 Epilogue ........................................... 1212
References ............................................... 1214
21 Concepts in High Temperature Superconductivity
E.W. Carlson, V.J. Emery, S.A. Kivelson, and D. Orgad .... 1225
21.1 Introduction ....................................... 1227
21.2 High Temperature Superconductivity is Hard to
Attain ............................................. 1230
21.3 Superconductivity in the Cuprates: General
Considerations ..................................... 1234
21.4 Preview: Our View of the Phase Diagram ............. 1244
21.5 Quasi-ID Superconductors ........................... 1245
21.6 Quasi-ID Physics in a Dynamical Stripe Array ....... 1257
21.7 Electron Fractionalization in D > 1 as
a Mechanism of High Temperature
Superconductivity .................................. 1259
21.8 Superconductors with Small Superfluid Density ...... 1262
21.9 Lessons from Weak Coupling ......................... 1272
21.10 Lessons from Strong Coupling ....................... 1277
21.11 Lessons from Numerical Studies of Hubbard and
Related Models ..................................... 1286
21.12 Doped Antiferromagnets ............................. 1300
21.13 Stripes and High Temperature Superconductivity ..... 1310
References ............................................... 1327
22 A Spin Fluctuation Model for d-Wave Superconductivity
A.V. Chubukov, D. Pines, and J. Schmalian ................ 1349
22.1 Introduction and Overview .......................... 1349
22.2 Spin-Fermion Model ................................. 1358
22.3 Summary of Strong-Coupling Theory for Electron-
Phonon Pairing ..................................... 1363
22.4 Strong-Coupling Approach to Spin-Fermion
Interaction ........................................ 1366
22.5 Fingerprints of Spin Fermion Pairing ............... 1377
22.6 Comparison with the Experiments on Cuprates ........ 1389
22.7 Conclusions ........................................ 1403
22.8 Note Added ......................................... 1405
References ............................................... 1407
23 Electronic Theory for Superconductivity in High-Tc
Cuprates and Sr2RuO4
D. Manske, I. Eremin, and К.H. Bennemann ................. 1415
23.1 Introduction ....................................... 1416
23.2 Electronic Theory for Hole-Doped and Electron-
Doped Cuprates ..................................... 1428
23.3 Electronic Theory for Ruthenates (Sr2RuO4) ......... 1451
23.4 Results for Hole-Doped and Electron-Doped
Cuprates ........................................... 1460
23.5 Results for Sr2RuO4 ................................ 1485
23.6 Summary and Outlook ................................ 1496
Appendix ................................................. 1497
References ............................................... 1511
24 Superfluid 3He and the Cuprate Superconductors
A.J. Leggett ............................................. 1517
24.1 Introduction: Bose Condensation and Cooper
Pairing ............................................ 1517
24.2 The Normal State: Is the Fermi-Liquid Picture
Valid? ............................................. 1522
24.3 Response Functions: The MIR Peak in the
Cuprates ........................................... 1525
24.4 The Cooper-Paired States of Superfluid 3He and
the Cuprates: General Considerations ............... 1526
24.5 Symmetry of the Order Parameter .................... 1531
24.6 Conclusion ......................................... 1534
24.7 Summary ............................................ 1534
References ............................................... 1535
Author Index ................................................. 1537
Subject Index ................................................ 1545
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