DeutschesFachbuch.de : Quantum Theory of Conducting Matter Newtonian Equations of Motion for a Bloch Electron Von Shigeji Fujita, Kei Ito

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Contents
Preface
v
Constants, Signs, Symbols, and General RemarksXIII
I Preliminaries 1
1 Introduction 3
1.1 Crystal Lattices 3
1.2 Theoretical Background 5
1.2.1 Metals and Conduction Electrons 5
1.2.2 Quantum Mechanics 6
1.2.3 Heisenberg Uncertainty Principle 6
1.2.4 Bosons and Fermions 7
1.2.5 Fermi and Bose Distribution Functions 7
1.2.6 Composite Particles 7
1.2.7 Quasifree Electron Model 8
1.2.8"Electrons" and "Holes"8
2 Lattice Vibrations and Heat Capacity 11
2.1 Einstein's Theory of Heat Capacity 11
2.2 Debye's Theory of Heat Capacity 15
3 Free Electrons and Heat Capacity 25
3.1 Free Electrons and the Fermi Energy 25
3.2 Density of States 30
3.3 Qualitative Discussions 36
3.4 Quantitative Calculations 38
4 Electric Conduction and the Hall Effect 43
4.1 Ohm's Law and Matthiessen's Rule 43
4.2 Motion of a Charged Particle in Electromagnetic Fields 46
4.3 The Landau States and Levels 48
4.4 The Degeneracy of the Landau Levels 51
4.5 The Hall Effect: "Electrons" and "Holes"56
5 Magnetic Susceptibility 61
5.1 The Magnetogyric Ratio 61
5.2 Pauli Paramagnetism 64
5.3 Landau Diamagnetism 67
6 Boltzmann Equation Method 75
6.1 The Boltzmann Equation 75
6.2 The Current Relaxation Rate 78
II Bloch Electron Dynamics 83
7 Bloch Theorem 85
7.1 The Bloch Theorem 85
7.2 The Kronig-Penney Model 91
8 The Fermi Liquid Model 97
8.1 The Self-consistent Field Approximation 97
8.2 Fermi Liquid Model 99
9 The Fermi Surface 103
9.1 Monovalent Metals (Na, Cu)103
9.2 Multivalent Metals 107
9.3 Electronic Heat Capacity and Density of States 111
10 Bloch Electron Dynamics 115
10.1 Introduction 115
10.2 Newtonian Equations of Motion 117
10.3 Discussion 123
III Applications. Fermionic Systems (Electrons)131
11 De Haas-Van Alphen Oscillations 133
11.1 Onsager's Formula 133
11.2 Statistical Mechanical Calculations: 3 D 139
11.3 Statistical Mechanical Calculations: 2 D 142
11.4 Two-Dimensional Conductors 147
12 Magnetoresistance 151
12.1 Introduction 151
12.2 Anisotropic Magnetoresistance in Cu 153
12.3 Shubnikov-De Haas Oscillations 155
12.4 Heterojunction GaAs/AlGaAs 161
13 Cyclotron Resonance 171
13.1 Introduction 171
13.2 Cyclotron Resonance in Ge and Si 172
13.3 Cyclotron Resonance in Al 184
13.4 Cyclotron Resonance in Pb 188
13.5 Cyclotron Resonance in Zn and Cd (HCP)192
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Index 2 D structure, 148
Aabsolute value, 213
aluminum, 107, 110
analytic, 92
angle of deflection, 159
angular frequency, 89, 135, 172
angular momentum, 61, 97
angular momentum quantum number, 97
anisotropic masses, 175
apparent effective mass, 178
atomic orbital, 98
Azbel-Kaner (AK) geometry, 184, 185
Bbalanced force equation, 214
band edge, 92, 94
band index, 87
band structure, 111
band theory of electrons, 100
bare lattice (potential), 99, 100
belly, 135
beryllium, 107, 108
Bloch electron (wave packet), 88, 115, 116, 118, 123
Bloch electron dynamics, 115, 118
Bloch quantum number, 123
Bloch theorem, 85-91, 100, 117, 147, 175
Bloch wave function, 87
body-center atom, 184
body-centered cubic (BCC) lattice, 3, 103, 182, 184
Bohr magneton, 63
Bohr-Sommerfeld quantization rule, 136
Boltzmann equation, 75, 77, 156, 159
Boltzmann equation method, 75-78
Boltzmann i 7-function, 78
Bose-Einstein condensation, 166
bosonic carrier, 215
bound state, 153
Bravais (lattice) vector, 89, 117
Brillouin boundary, 87, 90, 106
Brillouin zone, 104
bulk modulus, 19
Ccanonical momentum, 17, 219
canonical-ensemble average, 18
carrier charge sign, 200
center of a wave packet, 118
center of mass, 97
centripetal force, 127
Cerne et al., 205
charge current density, 44, 57
chemical potential, 27, 39, 67, 157
circular dichroism = optical ellipticity, 205
circularly polarized laser, 171
circularly polarized microwave, 173
circulating speed, 172
circulation, 50
classical formula for Seebeck coefficient, 196
clockwise, 125
closed Fermi curve, 128
closed orbit, 136, 154
collision term, 76
composite (c-) boson, 166
composite (c-) fermion, 166, 168
composite (c-) particle, 164
Compton scattering, 123
conducting plane, 175
conduction electron ("electron, " "hole"), 133, 197
conductivity, 197
conservation law, 124
constant-energy surface, 120
continuous, 92
continuous elastic body, 15
conversion rule, 211
Cooper pair, 138, 215
copper, 105, 155
copper plane, 129
core electron, 103
cosine law formula, 148, 186
coulomb attraction, 97
coulomb interaction, 78
counterclockwise, 125
CP = cyclotronic plane, 179
crystal lattice, 3, 11
crystalline state, 103
cube-edge atom, 183, 184
cubic lattice language, 182
cuprate superconductor, 129
current density, 161
curvature, 129, 153
cusp, 124
cyclotron frequency, 46, 163, 172, 175
cyclotron mass, 151, 153, 156, 164
cyclotron motion, 49, 164
cyclotron radius, 47
cyclotron resonance (CR), 50, 171181
cyclotronic plane (CP), 177
Dd-electrons, 107
de Haas, 155
de Haas and van Alphen (dHvA), 134
de Haas-van Alphen effect (oscillation), 133
de Haas-van Alphen effect (oscillation), 133, 134, 145
Deaver, 138
Debye, 15, 20
Debye frequency, 20
Debye T 3 law, 22
Debye temperature, 21, 23
Debye's model (theory), 15-23
decay rate, 141, 160
decomposition into sublattices, 182
degeneracy, 51
degenerate, 98
density of states, 18, 19, 20, 30-34, 36, 65, 111-113, 142, 157
density of states in energy, 37
dHvA oscillation, 145, 164
diamagnetic moment, 67
diamond (lattice) structure, 177
diamondlike crystal, 176
differential cross section, 76
diffusely, 45
diffusion coefficient, 199
Dingle, 164
Dingle temperature, 164
Dirac, 6, 118
Dirac delta-function, 71
Dirac delta-function replacement formula, 157, 159
dispersion relation, 89, 92, 117
distribution function, 159
divalent, 107
divalent metal, 107
DKK formula, 172, 174
Doll, 138
doping, 129
down spin, 63, 64
dressed electron, 153, 158, 164
Dresselhaus, 172
Dresselhaus, Kip, and Kittel (DKK), 172
drift velocity, 47, 48, 57, 209
Drude equation, 211
Dulong-Petit's law, 3, 23
dynamic = frequency dependent, 210
dynamic conductivity, 212
dynamic equilibrium, 6 dynamic Hall angle, 208
dynamic Hall relaxation rate, 212
dynamic rait, 212
Eeffective lattice potential, 100
effective magnetic field, 168
effective mass, 92, 119, 129, 172, 197
Ehrenfest-Oppenheimer-Bethe's rule, 165
eight columns, 98
Einstein, 11, 14
Einstein relation, 195, 201
Einstein's model, 11-14
electric conduction, 43
electric current, 195
electric current density, 75, 195, 209
electric field, 217
electromagnetic field, 46, 118
electromagnetic force, 217
electromotive force, 196 "electron, " 8, 48, 56, 125, 133, 171, 172, 179, 198, 204
electron heat capacity, 38 "electron"-like, 190
electron-phonon interaction, 101
electron spin resonance, 63, 64
electron-impurity system, 75
electronic heat capacity, 38, 111, 117
elementary fermion, 165
ellipse, 134
ellipsoid, 135
ellipsoidal Fermi surface, 136, 172
elliptic polarization, 206
energy band, 87
energy conservation law, 123
energy eigenvalue, 18
energy gap, 90
energy-dependent current relaxation rate, 82
energy-momentum relation, see dispersion relation
energy-time uncertainty principle, 163
envelope of the oscillations, 141, 151
equipartition theorem, 11
Euler's equations of motion for a rigid body, 124
excited electron, 111
Fface-center atom, 183
face-centered cubic (FCC) lattice, 3, 103
Fair bank, 138
Faraday geometry, 205, 206
Faraday rotation angle, 205, 206
Fermi cylinder, 136
Fermi-Dirac statistics, 36, 38, 100
Fermi distribution function, 26, 36, 68, 78, 156, 197
Fermi energy, 27
Fermi liquid model, 99-101, 117
Fermi momentum, 28
Fermi sphere, 30, 113
Fermi surface, 103-113, 125, 192
Fermi temperature, 30, 36, 42
Fick's law, 199 filling factor, 165, 166 first Brillouin zone, 104 fixed-end boundary...
flux quantum, 134, 136
fluxon, 166, 168
force term, 76
free electron, 25, 123
free energy, 67
free-particle wave function, 88
Fujita, 209
functional equation, 86
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