1 Historical perspective ..................................... 1
2 Electronic states, phonons, and electron-phonon
interaction ................................................ 5
2.1 Adiabatic approximation: Hamiltonian ....................... 5
2.2 Adiabatic approximation and non-adiabaticity: Born-
Oppenheimer and "crude" approaches ......................... 6
2.3 Electron-phonon coupling ................................... 9
2.4 Electron-phonon interaction and renormalization of normal
parameters ................................................ 11
2.5 The "Migdal" theorem ...................................... 15
2.6 Polaronic states .......................................... 16
2.6.1 Concept ............................................ 16
2.6.2 Dynamic polaron .................................... 17
3 Phonon mechanism .......................................... 20
3.1 Superconductivity as a "giant" non-adiabatic phenomenon ... 20
3.2 The BCS model ............................................. 21
3.3 Phonon mechanism: main equations .......................... 22
3.4 Critical temperature ...................................... 26
3.4.1 Weak coupling ...................................... 26
3.4.2 Intermediate coupling (λ  1.5) ................... 28
3.4.3 Coulomb interaction ................................ 29
3.4.4 Very strong coupling ............................... 31
3.4.5 The general case ................................... 33
3.4.6 About an upper limit of Tc ......................... 35
3.5 Properties of superconductors with strong coupling ........ 36
3.6 The Van Hove scenario ..................................... 39
3.7 Bipolarons: ВЕС versus BCS ................................ 39
3.8 Superconducting semiconductors ............................ 40
3.9 Polaronic effect and its impact on Tc ..................... 42
3.9.1 Double-well structure .............................. 42
3.9.2 Superconducting state .............................. 44
4 Electronic mechanisms ..................................... 47
4.1 The Little model .......................................... 47
4.2 "Sandwich" excitonic mechanism ............................ 50
4.3 Three-dimensional systems: electronic mechanism ........... 50
4.4 Plasmons .................................................. 52
4.4.1 Plasmons in layered systems: dispersion law
and "electronic sound" ............................. 53
4.4.2 Plasmons in layered conductors: pairing ............ 57
4.4.3 The 3D case: "demons" .............................. 58
5 Magnetic mechanism ........................................ 59
5.1 Introduction .............................................. 59
5.1.1 Localized versus itinerant aspects of the
cuprates ........................................... 60
5.2 Fermi liquid-based theories ............................... 62
5.2.1 The spin-bag model of Schrieffer, Wen, and Zhang
(1989) ............................................. 62
5.2.2 The t-J model (Emery, 1987; Zhang and Rice, 1988) .. 66
5.2.3 Two-dimensional Hubbard model studies by Monte
Carlo techniques ................................... 70
5.2.4 Spiral phase of a doped quantum antiferromagnet
(Shraiman and Siggia, 1988-89) ..................... 77
5.2.5 Slave bosons ....................................... 82
5.3 Non-Fermi-liquid models ................................... 85
5.3.1 The resonant valence bond (RVB) model and its
evolution .......................................... 85
5.3.2 Anyon models and fractional statistics ............. 86
5.4 Conclusions ............................................... 87
6 Experimental methods: Spectroscopic ....................... 88
6.1 Tunneling spectroscopy .................................... 88
6.1.1 Experimental method ................................ 88
6.1.2 Energy gap and transition temperature .............. 90
6.1.3 Inversion of the gap equation and α2F(Ω) ........... 91
6.1.4 Electron-phonon coupling parameter λ ............... 94
6.2 Scanning tunneling microscopy and spectroscopy ............ 96
6.3 Infrared spectroscopy ..................................... 97
6.4 Ultrasonic attenuation .................................... 99
6.5 Angle-resolved photoemission ............................. 100
6.6 Muon spin resonance (μtSR) ............................... 100
6.6.1 μSR studies of superconductivity .................. 102
7 Multigap superconductivity ............................... 103
7.1 Multigap superconductivity: general picture .............. 103
7.2 Critical temperature ..................................... 104
7.3 Energy spectrum .......................................... 105
7.4 Properties of two-gap superconductors .................... 108
7.4.1 Penetration depth; surface resistance ............. 108
7.4.2 Strong magnetic field: Ginzburg-Landau equations
for a multigap superconductor ..................... 110
7.4.3 Heat capacity ..................................... 111
7.4.4 Experimental data ................................. 111
7.5 Induced two-band superconductivity ....................... 112
7.6 Symmetry of the order parameter and multiband
superconductor ........................................... 113
8 Induced superconductivity: proximity effect .............. 114
8.1 Proximity "sandwich" ..................................... 114
8.2 Critical temperature ..................................... 115
8.3 Proximity effect versus the two-gap model ................ 119
8.4 Pair-breaking: gapless superconductivity ................. 119
9 Isotope effect ........................................... 122
9.1 General remarks .......................................... 122
9.2 Coulomb pseudopotential .................................. 122
9.3 Multi-component lattice .................................. 123
9.4 Anharmonicity ............................................ 123
9.5 Isotope effect in proximity systems ...................... 124
9.6 Magnetic impurities and isotope effect ................... 125
9.7 Polaronic effect and isotope substitution ................ 126
9.8 Penetration depth: isotopic dependence ................... 128
10 Cuprate superconductors .................................. 131
10.1 History .................................................. 131
10.2 Structure of the cuprates ................................ 132
10.3 Preparation of bulk and film cuprates .................... 133
10.4 Properties of the cuprates ............................... 134
10.4.1 Phase diagram ..................................... 134
10.4.2 Critical field Hc2 ................................ 135
10.4.3 Two-gap spectrum .................................. 136
10.4.4 Symmetry of the order parameter ................... 136
10.5 Isotope effect ........................................... 138
10.5.1 Polaronic state ................................... 138
10.5.2 Isotopic dependence of the penetration depth ...... 140
10.6 Mechanism of high Tc ..................................... 140
10.7 Proposed experiment ...................................... 145
11 Inhomogeneous superconductivity and the "pseudogap"
state of novel superconductors ........................... 147
11.1 "Pseudogap" state: main properties ....................... 148
11.1.1 Anomalous diamagnetism above Tc ................... 148
11.1.2 Energy gap ........................................ 150
11.1.3 Isotope effect .................................... 152
11.1.4 "Giant" Josephson effect .......................... 152
11.1.5 Transport properties .............................. 153
11.2 Inhomogeneous state ...................................... 154
11.2.1 Qualitative picture ............................... 154
11.2.2 The origin of inhomogeneity ....................... 155
11.2.3 Percolative transition ............................ 156
11.2.4 Inhomogeneity: experimental data .................. 156
11.3 Energy scales ............................................ 157
11.3.1 Highest-energy scale (T*) ......................... 158
11.3.2 Diamagnetic transition (Tc*) ...................... 158
11.3.3 Resistive transition (Tc) ......................... 159
11.4 Theory ................................................... 159
11.4.1 General equations ................................. 160
11.4.2 Diamagnetism ...................................... 160
11.4.3 Transport properties; "giant" Josephson effect .... 162
11.4.4 Isotope effect .................................... 166
11.5 Other systems ............................................ 167
11.5.1 Borocarbides ...................................... 167
11.5.2 Granular superconductors; Pb+Ag system ............ 167
11.6 Ordering of dopants and potential for room-temperature
superconductivity ........................................ 168
11.7 Remarks .................................................. 171
12 Manganites ............................................... 172
12.1 Introduction ............................................. 172
12.2 Electronic structure and doping .......................... 173
12.2.1 Structure ......................................... 173
12.2.2 Magnetic order .................................... 176
12.2.3 Double-exchange mechanism ......................... 176
12.2.4 Colossal magnetoresistance (CMR) .................. 177
12.3 Percolation phenomena .................................... 178
12.3.1 Low doping: transition to the ferromagnetic
state at low temperatures ......................... 178
12.3.2 Percolation threshold ............................. 179
12.3.3 Increase in temperature and percolative
transition ........................................ 180
12.3.4 Experimental data ................................. 181
12.3.5 Large doping ...................................... 182
12.4 Main interactions: Hamiltonian ........................... 183
12.5 Ferromagnetic metallic state ............................. 184
12.5.1 Two-band spectrum ................................. 184
12.5.2 Heat capacity ..................................... 186
12.5.3 Isotope substitution .............................. 187
12.5.4 Optical properties ................................ 189
12.6 Insulating phase ......................................... 190
12.6.1 Parent compound ................................... 190
12.6.2 Low doping: polarons .............................. 191
12.7 Metallic A-phase: S-N-S Josephson effect ............ 193
12.7.1 Magnetic structure ................................ 193
12.7.2 Josephson contact with the A-phase barrier ........ 193
12.8 Discussion: manganites versus cuprates ................... 195
13 Novel superconducting systems ............................ 197
13.1 Fe-based pnictide and chalcogenide superconductors ....... 197
13.2 Magnesium diboride: MgB2 ................................. 199
13.3 A-15 structure superconductors ........................... 201
13.4 Granular superconductors ................................. 202
13.5 S2RuO4: a very novel superconductor ...................... 203
13.6 Ruthenium cuprates ....................................... 204
13.7 Intercalated nitrides: self-supported superconductivity .. 205
14 Organic superconductivity ................................ 206
14.1 History .................................................. 206
14.2 Organic superconductors: structure, properties ........... 207
14.3 Intercalated materials ................................... 210
14.4 Fьllendes ................................................ 212
14.5 Small-scale organic superconductivity .................... 213
14.6 Pair correlation in aromatic molecules ................... 214
15 Pairing in nanoclusters: nano-based superconducting
tunneling networks ....................................... 218
15.1 Clusters: shell structure ................................ 218
15.2 Pair correlation ......................................... 220
15.2.1 Qualitative picture ............................... 220
15.2.2 Main equations: critical temperature .............. 222
15.2.3 Energy spectrum; fluctuations ..................... 225
15.3 How to observe the phenomenon? ........................... 226
15.4 Cluster-based tunneling network: macroscopic
superconductivity ........................................ 227
15.5 Cluster crystals ......................................... 228
Appendices .................................................... 229
Appendix A: Diabatic representation ........................ 229
Appendix B: Dynamic Jahn Teller effect ..................... 231
References .................................................... 233
Index ......................................................... 255
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