DeutschesFachbuch.de : Introduction to Solid-State Theory Von Otfried Madelung

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Contents
1.Fundamentals
1.1 Introduction 1
1.2 The Basic Hamiltonian 6
1.3 The Hartree-Fock Approximation 10
2.The One-Electron Approximation
2.1 The Electron Gas Without Interaction 17
2.1.1 Introduction 17
2.1.2 The Energy States 18
2.1.3 Excited States 20
2.1.4 The Fermi Distribution 24
2.1.5 Free Electrons in an Electric Field 28
2.1.6 Free Electrons in a Magnetic Field 30
2.1.7 Diaand Paramagnetism of Free Electrons, the de Haasvan Alphen Effect 3...
2.2 Electrons in a Periodic Potential 36
2.2.1 Introduction 36
2.2.2 The Symmetries of the Crystal Lattice 38
2.2.3 The Schrödinger Equation for Electrons in a Periodic Potential 42
2.2.4 The Reciprocal Lattice, Bragg Reflections 42
2.2.5 Consequences of Translational Invariance 45
2.2.6 Nearly Free Electron Approximation 50
2.2.7 Wannier Functions, LCAO Approximation 53
2.2.8 General Properties of the Function E"(k)55
2.2.9 Dynamics of Crystal Electrons 59
2.2.10 The Density of States in the Band Model 66
2.2.11 The Band Structure of Metals, Fermi Surfaces 67
2.2.12 The Band Structure of Semiconductors and Insulators 75
2.2.13 Consequences of the Invariance of the Hamiltonian to Symmetry Operati...
2.2.14 Irreducible Representations of Space Groups 82
2.2.15 Spin, Time Reversal 89
2.2.16 Pseudopotentials 91
3.Elementary Excitations
3.1 The Interacting Electron Gas: Quasi-Electrons and Plasmons 96
3.1.1 Introduction 96
3.1.2 The Coulomb Interaction 96
3.1.3 The Hartree-Fock Approximation for the Electron Gas 101
3.1.4 Screening, Plasmons 103
3.1.5 Quasi-Electrons 110
3.1.6 The Dielectric Constant of the Electron Gas 114
3.2 Electron-Hole Interaction in Semiconductors and Insulators: Excitons 118
3.1.1 Introduction 118
3.2.2 The Ground State of the Insulator in Bloch and Wannier Representation...
3.2.3 Excited States, the Exciton Representation 120
3.2.4 Wannier Excitons 123
3.2.5 Frenkel Excitons 126
3.2.6 Excitons as Elementary Excitations 127
3.3 Ion-Ion Interaction: Phonons 129
3.3.1 Introduction 129
3.3.2 The Classical Equations of Motion 130
3.3.3 Normal Coordinates, Phonons 136
3.3.4 The Energy Content of the Lattice Vibrations, Specific Heat 139
3.3.5 Calculation of Phonon Dispersion Relations 143
3.3.6 The Density of States 148
3.3.7 The Long Wavelength Limit: Acoustic Branch 150
3.3.8 The Long Wavelength Limit: Optical Branch 153
3.4 Spin-Spin Interaction: Magnons 155
3.4.1 Introduction 155
3.4.2 Spin Waves in Ferromagnets: Magnons 156
3.4.3 Spin Waves in Lattices with a Basis, Ferri-, and Antiferromagnetism 16...
3.4.4 Ferromagnetism Near the Curie Temperature
166
3.4.5 Ordered Magnetism of Valence and Conduction Electrons, the Collective ...
4.Electron-Phonon Interaction: Transport Phenomena
4.1 The Interaction Processes 175
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Subject Index
AAbsorption 261
- by free charge carriers 284-289
- exciton 278-281
- in a magnetic field 289-294
- in a superconductor 241
- two-photon 276, 277
Absorption coefficient 262, 266
Absorption edge 269, 282
Absorption spectra
- of Ge 282, 284, 286, 289
- of superconducting In 241
- of ZnO 286
Accidental degeneracy 89
Acoustic branch 135, 150
Acoustic phonon 139
Activator 411
Adiabatic approximation 9
Alkali metals, band structure 70
Allowed transitions 270, 281
Alloy 443, 447
Alloy scattering 447
Aluminium:
- band structure 70
- Fermi surfaces 71
Amorphous semiconductors 444, 447, 454
Anderson transition 365, 443
Anharmonicity of lattice vibrations 130, 308, 320-322
Anisotropy field 164
Antibonding state 333
Antiferromagnetic magnons 165
Antiferromagnetism 157, 163- 167
Anti-Stokes scattering 311
Atomic force constants 131
Atomic orbitals 330, 331, 334
Auger recombination 409
Azbel-Kaner resonance 299
BBand conduction 375
Band structure 49
- alkali metals 70
- GaSe 345
- Ge, in magnetic field 294
- metals 67-75
- semiconductors and insulators 75-80
- Si 76
Bardeens self consistent potential 182
Basis 39
Basis vector 38
BCS theory 230
Bethe lattice 446
Bloch approximation 182
Bloch electron 37, 48, 113
Bloch function 48, 53, 57
Bloch representation 119
Bloch theorem 47, 48, 59
Bloch-Grüneisen relation 214
Bogoliubov-Valatin transformation 24, 233
Boltzmann equation 187-197
- for the electron system 190
- for the phonon system 190, 323
- limits of applicability 365
Bond, chemical 329-356
- covalent 335, 339
- delocalized 336-339, 352-356
- dielectric theory 347-352
- ionic 339
- ionic component 342, 350, 351
- ionicity 335, 342
- localized 331, 336-347
- metallic 339
- mixed covalent/ionic 342
- neutral 343
- polarity 334, 335
- polarization 341
- resonance 341
Bonding charge 349
Bonding length 341
Bonding state 333
Bora-Oppenheimer method 9
Born-von Karman boundary conditions 18
Bose distribution 139
Bose-Einstein condensation of excitons 128
Bound excitons 419-421
Boundary conditions, periodic 18, 58
Bragg reflections 42-45, 51, 61
Branch, acoustic and optical 135
Branches in the phonon spectrum 133
Bravais lattice 42
Breathing shell model 147
Bridgman relation 210
Brillouin function 168
Brillouin scattering 309
Brillouin zone 42, 81
- of cubic and hexagonal point lattices 68
- of the two-dimensional hexagonal lattice 45, 46, 49, 52
CCauchy relations 152
Character of a representation 84
Character table 87
Chemical bond, see Bond, chemical
Chemical potential 26, 196
Closed orbits 75, 223
Coherence length 249, 250, 251
Cohesive energy:
- of co valent crystals 340
- of ionic crystals 339
- of metals 353
Collective electron model 170
Collective excitations 3, 107, 113
- of the electron gas 104
- of the ion lattice 129
Combined density of states 269, 271
Complex dielectric constant 259-262, 266
Complex index of refraction 261
Compositional disorder 436
Conduction band 67, 76
Confîguration coordinate 373, 413-415
Cooper pair 230-233
- binding energy 235
Copper:
- density of states 171
- Fermi surfaces 71, 75
Correlation energy 354
Correlations 103, 229, 357-362
Coulomb interaction 96-101
- screened 108
Coulomb potential, short-range and long range components 105
Covalent bond 335, 339
Covalent radius 341
Creation and annihilation operators 458
- for electrons 22, 127
- for excitons 128
- for holes 23, 127
- for magnons 161
- for phonons 178
- for photons 254
- for polaritons 256
Creation of an electron-hole pair 175
Critical conductance 453
Critical magnetic field 244
Critical point 270, 271, 284, 286
Critical temperature 239
Crystal electron 37, 57
- dynamics 59-65
Crystal field theory 387-390
Crystal momentum 57
Cubic point lattice:
- Brillouin zone 68
- Wigner-Seitz cell 40
Curie constant 169
Curie law 169
Curie temperature 169
Curie-Weiss law 170
Cyclotron resonance 298
- frequency 32, 74, 294
DDangling bonds 437, 444
d-Bands 72, 357
de Broglic relation 28
Debye approximation 142, 148, 212
Debye frequency 141, 231
Debye length 421
Debye temperature 142
Deep defects 384
Defects 377-425
deep 384
- isoelectronic 419
- shallow 380
Defect statistics 397-401
Deformation potential 182
Degenerate electron gas 27
de Haas-van Alphen effect 33-36, 73, 74
Delocalized bond 336-339, 352-356
Delocalized state 4, 327
Density of states:
- combined 269, 271
- in a magnetic field 33, 34
- in a superconductor 242
- in disordered solids 442, 443-447
- in k-space 19
- in the band model 66, 67
- in the phonon spectrum 141, 148, 149
- on the energy scale 19, 34
Diamagnetism of free electrons 33-36
Dielectric constant:
- complex 259-262, 266
- effective 125
- frequency and wave number dependent 114
- frequency dependent 260
- high frequency 125, 154
- of the electron gas 114- 118
- static 125, 154
Dielectric theory of the covalent bond 347-352
Diffusion of lattice defects 406-409
Direct transitions 263, 266-271, 279
- in a magnetic field 290
Disorder 435-456
- equilibria 401-406
- types of 436, 437
Disordered lattices, transport in 447-456
Dispersion 261
- spatial 260
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