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
E. 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
L.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 x2-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.F-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
|
