Alexandrov A.S.,Theory of Superconductivity - From Weak to Strong Coupling
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296
Index
of charged Bose gas, 141
of two-component Bose gas, 145
Fermi energy, 173, 255
Fermi liquid
breakdown, 38
instability, 98
theories of high T
c
, 164
fluctuations, 15
fluctuation theory, 204
flux
expulsion, 40
quantization, 10
quantum, 10
free energy
London expression, 9
superfluid, 9
vortex, 23
Fr¨ohlich
–Coulomb Hamiltonian, 129
Hamiltonian, 77, 97
interaction, 77
observation, 33
polaron, 107
gap
in BCS superconductors, 41
in high T
c
oxides, 218
gapless superconductivity, 55
gauge transformation, 18
Gibbs energy, 17
Gi-number, 16
Ginzburg
–Landau equation, 14
–Landau parameter, 15
–Landau theory, 13
–Landau theory limitations, 15
golden rule, 43
Gor’kov
equations, 60, 64
formalism, 59
Green’s function
advanced, 65, 277
anomalous, 62, 85
electron, 78
formulation of BCS theory, 59
matrix, 86
Matsubara, 275
normal, 59
one-particle, 274
phonon, 79
retarded, 65
temperature, 277
Hall ratio, 5, 189
harmonic oscillator, 24
Hartree approximation, 75, 240
4
He, 158
3
He, 158
heat capacity
of BCS superconductors, 45
of high-T
c
oxides, 208
Hebel–Slichter peak
absence in high-T
c
oxides, 195
in BSC superconductors, 48, 49
Heisenberg
Hamiltonian, 136
operators, 53, 112, 275
high-T
c
superconductors, 162
Hosltein
–Hubbard model, 127
model, 99
polaron, 107
hopping, 95, 99
Hubbard U
infinite, 129
negative, 205
repulsive, 164
hyperfine interaction, 48, 194
incoherent background, 115
isotope effect
bipolaronic, 146, 206
in BCS superconductors, 44
on carrier mass, 206, 207
on penetration depth, 206
Index
297
Josephson
current, 30
effect, 32
kinetic mechanism, 163, 166
Knight shift, 195
Kohn–Luttinger, 91
Korringa law
breakdown, 195
in metals, 48
k · p perturbation theory, 247
Kosterlitz–Thouless temperature,
204
Landau
criterion, 28
diamagnetism, 257
theory, 13
Lang–Firsov transformation, 103
LDA, 74
Legendre polynomials
summation theorem, 51
Levinson theorem, 236
lifetime of quasi-particles, 234
localization length, 213
London
equation, 9
penetration depth, 9
theory, 6
Lorenz number, 192
mass
of small polaron, 111
renormalized, 84
tensor, 5
Matsubara
frequencies, 86
operators, 62, 275
Maxwell
equation, 9
gauge, 8
McMillan formula, 90
Meissner–Ochsenfeld
effect, 7
effect in CBG, 148
experiment, 7
metal–ammonia solution, 11
Migdal
–Eliashberg theory, 88
–Eliashberg theory breakdown,
98
theorem, 88
mixture of condensates, 142
Monte Carlo algorithm, 109
Mott insulator, 163
multi-phonon correlator, 124
nearly Fermi liquid, 167
N´eel temperature, 165
neutron scattering, 167, 195, 242
non-Fermi-liquid theories
interlayer RVB, 164
Luttinger liquid, 164
marginal, 167
RVB, 164
nuclear
spin relaxation rate, 48, 194
Ogg’s pairs, 11
Ogg–Schafroth phenomenology, 12
operators
annihilation, 34, 268, 269
creation, 34, 268, 269
current density, 71
displacement, 75
field, 52, 271
identity, 113, 281
phonon, 75
order parameter
BCS, 35, 50
bipolaronic, 157
symmetry, 156
overcrowding, 183
overdoped cuprates, 183
overscreening, 34
pairing
collective, 167
298
Index
individual, 171
pairs
Bose, 11
Cooper, 12
Pauli
exclusion principle, 267
matrices, 86
pair-breaking limit, 25
paramagnetism, 257
partition function, 254
Peierls substitution, 138
Pekar equation, 239
perturbation expansion, 103
phase diagram, 182, 183
phase equation, 235
phase shift, 235
phonon frequency, 78
phonons, 77
phonon sidebands, 115
Pippard
equation, 12
limit, 13
non-local relation, 12
theory, 12
plasma
excitations, 33
frequency, 89, 117, 141
plasmon
acoustic, 144
ionic, 78
optical, 144
polaron
band, 102
band narrowing factor, 104
Bloch states, 95
collapse, 72
damping, 105
dynamics, 102
large, 95
level shift, 104
mass, 109, 110
radius, 101
small, 95
spectral function, 110
–phonon interaction, 111
–polaron interaction, 103, 116
polaronic
Fermi-liquid, 102
superconductivity, 119
pseudogap, 194, 195
pseudospin, 135
quantum phase transition, 167
quasi-particle spectrum, 142
resistivity
below T
c
, 188
in-plane, 183
out-of-plane, 195
response function, 117, 147
scattering
boson–acoustic phonon, 187
impurity, 187
of bosons, 186
resonance, 189
two-phonon, 106
self-energy
electron, 83
hole, 228
phonon, 79
second order, 82
self-trapping, 95
Slater determinant, 266
sound
attenuation, 46
damping, 81
velocity, 81
specific heat
anomaly, 207
fermions, 257
jump, 46
spectral function, 110, 228, 230,
276
spin bipolaron, 161
spin-flip scattering, 48
spin gap, 194
strings, 241
Index
299
stripes, 166, 239
strong coupling theory, 95
sum rule, 6, 276
supercurrent, 13
superfluid
density, 13
surface energy, 17
symmetry, 156
susceptibility
diamagnetic, 7
spin, 196
thermal conductivity
enhancement, 238
Hall, 192
of BCS superconductors, 49
of high T
c
cuprates, 192
thermally activated hopping, 95
tight-binding approximation, 249
time ordering, 63
t–J model, 164
Tolmachev logarithm, 163
transformation
Bogoliubov, 36
canonical, 279
Lang–Firsov, 103
transition
continuous, 17
second-order, 16
third-order, 17, 262
transmission, 221
tunnelling
conductance, 43
in high-T
c
cuprates, 219
Josephson, 29
single-electron, 41
SIS, 221
Type I, II superconductors, 20
uncertainty principle, 35
upper critical field
curvature, 156
of BCS superconductor, 23
of ideal Bose gas, 154
of interacting Bose gas, 154, 156
unconventional, 210
Van Hove scenario, 167
variational calculations, 111
vertex
corrections, 83
electron–phonon, 117
vortex
charged, 148, 152
core, 22
free energy, 23, 152
interaction, 27
lattice, 26
line, 20
pinning, 29
Wannier
orbitals, 96, 249
representation, 96
Wiedemann–Franz law, 192
Wigner crystallization, 118
Wigner cross section, 189, 237