Fundamentals of Condensed Matter Physics

Cover......Page 1
Half-title......Page 3
Title page......Page 5
Copyright information......Page 6
Dedication......Page 7
Table of contents......Page 9
Preface......Page 13
Part I Basic concepts: electrons and phonons......Page 17
1.1 Classification of solids......Page 19
1.2 A first model of a solid: interacting atoms......Page 20
1.3 A second model: elementary excitations......Page 22
1.4 Elementary excitations associated with solids and liquids......Page 23
1.5 External probes......Page 24
1.6 Dispersion curves......Page 25
1.8 Interactions among particles......Page 29
1.8.1 Quasiparticle–boson interactions......Page 31
1.8.2 Quasiparticle–quasiparticle interactions......Page 33
1.8.3 Collective excitation interactions......Page 34
2.1 General Hamiltonian......Page 36
2.2 The Born–Oppenheimer adiabatic approximation......Page 37
2.4 The periodic potential approximation......Page 38
2.5 Translational symmetry, periodicity, and lattices......Page 39
3.1 Free electron model......Page 47
3.2 Symmetries and energy bands......Page 49
3.2.1 Symmetries and energy bands in one dimension......Page 51
3.2.2 Energy bands and gaps: the Kronig–Penney model......Page 52
3.3 Nearly-free electron model......Page 55
3.4 Tight-binding model......Page 59
3.5 Electron (or hole) velocity in a band and the f-sum rule......Page 64
3.6 Periodic boundary conditions and summing over band states......Page 68
3.7 Energy bands for materials......Page 71
4.1 Lattice vibrations......Page 79
4.2 Second quantization and phonons......Page 87
4.3 Response functions: heat capacity......Page 93
4.4 Density of states......Page 95
4.4.1 The Debye approximation......Page 96
4.4.2 The Einstein spectrum......Page 99
4.5 Critical points and van Hove singularities......Page 100
Part I Problems......Page 107
Part II Electron interactions, dynamics, and responses......Page 115
5.1 Effective Hamiltonian and Wannier functions......Page 117
5.2 Electron dynamics in the effective Hamiltonian approach......Page 119
5.3 Shallow impurity states in semiconductors......Page 123
5.4 Motion in external fields......Page 124
5.5 Effective mass tensor......Page 129
5.6 Equations of motion, Berry phase, and Berry curvature......Page 130
6 Many-electron interactions: the homogeneous interacting electron gas and beyond......Page 135
6.1 The homogeneous interacting electron gas or jellium model......Page 137
6.2 Hartree–Fock treatment of the interacting electron gas......Page 139
6.3 Ground-state energy: Hartree–Fock and beyond......Page 142
6.4 Electron density and pair-correlation functions......Page 146
6.5 g(r, r) of the interacting electron gas......Page 148
6.6 The exchange-correlation hole......Page 151
6.7 The exchange-correlation energy......Page 152
7 Density functional theory (DFT)......Page 157
7.1 The ground state and density functional formalism......Page 158
7.2 The Kohn–Sham equations......Page 160
7.3 Ab initio pseudopotentials and density functional theory......Page 166
7.4 Some applications of DFT to electronic, structural, vibrational, and related ground-state properties......Page 168
8.1 Linear response theory......Page 175
8.2 Self-consistent field framework......Page 179
8.3 The RPA dielectric function within DFT......Page 180
8.4 The homogeneous electron gas......Page 182
8.5 Some simple applications......Page 185
8.6 Some other properties of the dielectric function......Page 189
Part II Problems......Page 194
Part III Optical and transport phenomena......Page 199
9.1 Response functions......Page 201
9.2 The Drude model for metals......Page 205
9.3 The transverse dielectric function......Page 208
9.4 Interband optical transitions in semiconductors and insulators......Page 212
9.5 Electron–hole interaction and exciton effects......Page 217
9.5.1 Weak binding limit in the two-band model......Page 221
9.5.2 Excitonic effects in the isotropic two-band model......Page 226
10.1 The rigid-ion model......Page 236
10.2 Electron–phonon matrix elements for metals, insulators, and semiconductors......Page 240
10.3 Polarons......Page 245
11.1 Free electrons in a uniform magnetic field and Landau levels......Page 251
11.2 Crystal electrons in a static B-field......Page 253
11.2.1 Semiclassical analysis......Page 254
11.3 Effective mass and real-space orbits......Page 255
11.3.1 A geometric expression for m*......Page 256
11.4 Quantum oscillations: periodicity in 1/B and the de Haas–van Alphen effect in metals......Page 257
12.1 Elementary treatment of magnetoresistance and the Hall effect......Page 264
12.1.1 One-carrier-type model......Page 266
12.1.2 Two-carrier-type model......Page 267
12.1.3 Influence of open orbits in high field......Page 270
12.2.1 The phenomenon......Page 273
12.2.2 Experimental setup......Page 274
12.2.3 Two-dimensional magnetoresistance in the quantum limit......Page 276
12.2.4 Effects of random impurities and defects......Page 277
12.2.5 Gauge argument......Page 278
12.3 The Boltzmann equation formalism and transport in real materials......Page 280
12.3.2 Equation of motion for f(k, r, t)......Page 281
12.3.3 Steady-state transport......Page 283
12.3.4 Relaxation time approximation......Page 285
12.4.1 Isothermal electrical conductivity......Page 287
12.4.2 Thermo-electric transport......Page 288
12.4.3 Heat current......Page 289
12.4.4 Thermal conductivity......Page 290
12.4.5 Examples of thermo-electric effect......Page 291
Part III Problems......Page 294
Part IV Many-body effects, superconductivity,magnetism, and lower-dimensional systems......Page 301
13.1 General formalism......Page 303
13.2 Interacting Green's functions......Page 307
13.3 Feynman diagrams and many-body perturbation theory techniques......Page 314
14.1 Brief discussion of the experimental background......Page 321
14.2.1 London theory......Page 327
14.2.2 Ginzburg–Landau theory......Page 330
14.2.3 Microscopic theory......Page 341
14.3 Superconducting quasiparticle tunneling......Page 365
14.4 Spectroscopies of superconductors......Page 372
14.5 More general solutions of the BCS gap equation......Page 376
14.6 Field theoretical methods and BCS theory......Page 384
15.2 Diamagnetism......Page 388
15.3 Paramagnetism......Page 390
15.4 Ferromagnetism and antiferromagnetism......Page 393
15.5 Magnetism in metals......Page 402
15.6 Magnetic impurities and local correlation effects......Page 405
16.1 Density of states and optical properties......Page 409
16.2 Ballistic transport and quantization of conductance......Page 415
16.3 The Landauer formula......Page 420
16.4 Weak coupling and the Coulomb blockade......Page 422
16.5 Graphene, carbon nanotubes, and graphene nanostructures......Page 425
16.5.1 The π-band electronic structure and 2D Dirac fermions in graphene......Page 427
16.5.2 The Dirac Hamiltonian......Page 430
16.5.3 Graphene Nanostructures......Page 431
16.6 Other quasi-2D materials......Page 437
Part IV Problems......Page 440
References......Page 450
Index......Page 456