Haug H., Koch S. Quantum theory of the optical and electronic properties of semiconductors
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January 26, 2004 16:26 WSPC/Book Trim Size for 9in x 6in b ook2
Index 449
intraband relaxation, 226
intraband transitions, 393, 394
intrinsic optical bistability, 317
intrinsic semiconductor photon echo,
275
inversion factor, 285
ion–ion interaction, 109
ionization continuum, 290
jellium approximation, 152
jellium model, 107
Keldysh contour, 404
Keldysh Green’s function, 401
Keldysh indices, 407
ket-vector, 66
kinetic properties, 163
k · p theory, 41
Kramers–Kronig relation, 6
Kramers–Kronig transformation, 302
ladder approximation, 404
Lagrange functional, 421
Lagrangian, 425
Lagrangian density, 423
Landau ladder, 375
Landau states, 374
Lang–Kobayashi equations, 342
Langevin equation, 328, 329
Langreth theorem, 405, 439
Laplace operator, 172
laser diodes, 321
laser frequency, 327
laser spectrum, 340
laser threshold, 327
lattice matched conditions, 60
lattice potential, 29
lattice vector, 30
reciprocal, 31
Levi–Civita tensor, 423
light emission, 323
light-emitting diodes, 321
light-hole band, 46
light-induced shift, 236
Lindhard formula, 139, 140
line-shape theory, 412
line-width enhancement factor, 338,
341
linear polarization, 397
linear response theory, 20
Liouville equation, 70, 395
localization energy, 61
logic functions, 316
long wave-length limit, 134
long-time limit, 228
longitudinal eigenmodes, 139, 197
longitudinal optical phonons, 222
longitudinal relaxation time, 76
longitudinal wave equation, 307
longitudinal-transverse splitting, 197
Lorentz force, 371, 374
Lorentzian line shape, 8
low excitation regime, 216
luminescence spectrum, 379
Luttinger Hamiltonian, 47
Luttinger parameters, 47
magnetic field, 374
magneto-excitons, 371
magneto-luminescence, 378
magneto-plasma, 371, 375
many-body Hamiltonian, 434
Markov approximation, 218, 264, 331,
408
Markovian noise, 336
Markovian scattering kinetics, 227
Maxwell’s equations, 9, 424
mean-field Hamiltonian, 225
memory function, 4
memory structure, 227
mesoscopic scale, 35
mesoscopic structures, 384
mesoscopic systems
Coulomb interaction, 55
metal, 41
microcavity, 206
microcavity polariton, 207
microcrystallites, 383
mixing
heavy- and light hole, 62
mode pulling, 327
Mott criterion, 299
January 26, 2004 16:26 WSPC/Book Trim Size for 9in x 6in b ook2
450 Quantum Theory of the Optical and Electronic Properties of Semiconductors
Mott density, 286, 290
multi-subband Bloch equations, 221
multi-subband situation, 123
multiband configuration, 256
multilevel Bloch equations, 396
narrow band-gap semiconductors, 291
nearly free electron model, 50
non-Markovian quantum kinetics, 227
nonlinear optical response, 310
nonlinearity
density-dependent, 307
nonradiative recombination, 324
number operator, 91
numerical matrix inversion, 289
Nyquist noise, 334
occupation number, 91
off-diagonal damping, 411
off-diagonal elements, 71
one-component plasma, 131
one-particle density matrix, 164
operator
contour-ordering, 436, 437
Fermion, 437
time-ordering, 436
optical bistability, 305, 311
optical Bloch equations, 24, 75
optical Bloch equations for quantum
dots, 395
optical dielectric function, 290
optical dipole matrix element, 69
optical dipole transition, 65, 68
optical feedback, 340
optical gain, 23, 85, 290, 399, 413
optical matrix element, 72, 197
optical nonlinearities, 86
optical polarization, 79, 169
optical pumping, 84
optical resonator, 311
optical response, nonlinear, 310
optical spectrum, 184, 300
optical Stark effect, 27, 237
optical Stark shift, 23
optical susceptibility, 2, 3, 21, 185,
295, 307, 356
atomic, 17
free carrier, 80
optical switching devices, 291
optical theorem, 406
optically thin samples, 271
orthogonality relation, 65
oscillations, coherent, 254
oscillator, 2
oscillator potential, 374
oscillator strength, 21, 186
oscillator strength sum rule, 22
overlap integral, 359
Pad´e approximation, 96, 294
pair correlation function, 118, 121
pair energy, 389
pair function, 165
pair wave function, 391
paraxial approximation, 307
particle propagator, 150
Pauli blocking, 219, 264
Pauli exclusion principle, 89
periodic boundary conditions, 34
perturbed free induction decay, 254
phase, 311, 341
phase-space filling, 219, 262
phonon Hamiltonian, 225
phonon-assisted density matrix, 224
phonons, 425
photon echo, 78, 275, 280
intrinsic, 275
photon operators, 430
photons, 422
picture
Heisenberg, 260, 436, 437
interaction, 260
plasma eigenmodes, 139
plasma frequency, 6, 134, 143
plasma screening, 137, 296
plasma theory, 296
plasmon, 129, 140
plasmon frequency, 147
effective, 146
plasmon pole, 416
plasmon–pole approximation, 146,
147, 158
January 26, 2004 16:26 WSPC/Book Trim Size for 9in x 6in b ook2
Index 451
Poisson’s equation, 138
polariton, 193
microcavity, 207
polariton branch, 204
polariton dispersion, 196, 199, 207
polariton Hamiltonian, 205
polariton operators, 203
polariton spectrum, 204
polarization, 2, 20
interband, 164
linear, 397
polarization diagram, 406
polarization equation, 261
polarization fluctuations, 334
polarization function, 133, 138, 405
polarization operator, 392
polaron shifts, 231
positive charge background, 108
power series expansion, 175
principal value, 5
probe susceptibility, 252
probe transmission, 249
pump rate, 323
pump–probe delays, 253
pump–probe experiment, 235
quantized states, 58
quantum beats, 274
quantum coherence, 218, 235
quantum confined Franz-Keldysh
spectrum, 357
quantum confinement, 55
quantum dot, 54, 383
Bloch equations, 395
quantum kinetics, 227
quantum wire, 54, 123, 189, 292, 372,
380
absorption spectrum, 190
thin, 180
quantum-dot Hamiltonian, 395
quantum-well band structure, 63
quantum-well structures, 53, 292
quasi-equilibrium, 73
quasi-equilibrium assumption, 168
quasi-equilibrium regime, 216
quasi-particles, 194
quasiclassical approximation, 361
Rabi flopping, 76
Rabi frequency, 25, 215
renormalized, 284
Rabi sidebands, 26
radial distributions, 391
radial equation, 298
radial exciton wave functions, 178
random phase approximation, 131,
167
rate equation, 310, 314, 322
reciprocal lattice vector, 31
recombination, nonradiative, 324
redshift, 236, 264
reduced density matrix, 165, 213, 219
reduced mass, 170
refraction, 6
refractive index, 322
relaxation oscillation, 337, 342
relaxation oscillation frequency, 342
relaxation times, 222
renormalized band gap, 281
renormalized energies, 155
renormalized frequencies, 168
renormalized single-particle energies,
215
representation
interaction, 436
reservoir, 329
resonator, 312, 325
resonator transmission, 313
retardation effects, 271
retarded Green’s function, 12, 149,
151, 414
retarded potential, 416
retarded self-energy, 154
rotating wave approximation, 25, 74
Rydberg energy, 177
scattering terms, 401
Schawlow–Townes line-width formula,
339
Schrödinger equation, 425
screened exchange self-energy, 157
screened potential, 405
January 26, 2004 16:26 WSPC/Book Trim Size for 9in x 6in b ook2
452 Quantum Theory of the Optical and Electronic Properties of Semiconductors
screening, 140
build-up, 413
Debye–Hückel, 142
Thomas–Fermi, 142
screening length, 141, 144
screening wave number, 141, 142
second Born approximation, 408, 409
second moments, 331
second quantization, 89, 110, 421, 425
selection rules, 43, 256
self-consistency equation, 295
self-energy, 108
Coulomb hole, 158
exchange, 154, 168
irreducible, 439
retarded, 154
screened exchange, 157
self-energy corrections, 231
self-sustained oscillations, 342
semiconductor, 41
semiconductor Bloch equations, 168,
211, 216
semiconductor microstructures, 53
shot noise, 334
sidemodes, 340
signal amplification, 316
single-particle energies, 213, 388, 390
renormalized, 215, 284
single-particle spectrum, 387
size distribution, 398
Sommerfeld factor, 190
spatial dispersion, 195, 198
spectral hole burning, 342
spectral properties, 163
spin echo, 275
spin–orbit interaction, 45
spontaneous emission, 323, 324, 333
Stark effect, dc, 349, 360
state mixing, 63
statistical operator, 90
stimulated emission, 323, 334
stochastic laser theory, 335
strained layer structures, 60
subband structure, 72
sum rule
oscillator strength, 22
superconductivity, 101
superfluidity, 101
surface charge, 385
surface polarization, 385
susceptibility, 290
electron–hole–pair, 186
optical, 2, 3, 21, 185, 307, 356
susceptibility component, 379
susceptibility function, 287, 309
susceptibility integral equation, 288
switching devices, 315
thermal distributions, 102
thin samples, 270, 271
thin wires, 180
Thomas–Fermi screening, 141, 142
tight-binding approximation, 36
tight-binding bands, 39
tight-binding wave function, 37
total carrier density, 309
transient transmission oscillations,
254
translation operator, 30
transmission resonator, 313
transverse eigenmodes, 195
transverse field equation, 308
transverse relaxation time, 76
transverse wave equation, 306
truncation scheme, 256
tunnel integral, 370
two electron–hole–pair excitations,
263
two-band approximation, 69
two-band model, 166
two-levelmodel,26
two-point density matrix, 269
two-pulse wave mixing, 269
type-I structures, 53
type-II structures, 53
ultrafast regime, 217
Urbach rule, 198
valence band, 40
valence bands, degenerate, 45
vector potential, 372
January 26, 2004 16:26 WSPC/Book Trim Size for 9in x 6in b ook2
Index 453
vertex correction, 404
vertex function, 289
vertex integral equation, 289
virial, 94
virtual excitations, 238
Wannier equation, 169, 171
Wannier excitons, 173, 193
Wannier functions, 36
wave equation, 9, 324
longitudinal, 307
transverse, 306
wave number, 10
wave propagation, 306
Whittaker functions, 183
Wigner distribution, 270
Wigner–Seitz cells, 32
WKB method, 360
Yukawa potential, 141
zero-point energy, 58, 82, 102