Quantum theory of the solid state: an introduction
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer Acad. Publ.
2004
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| Series: | Fundamental theories of physics
136 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXV, 626 S. Ill., graph. Darst. |
| ISBN: | 1402018215 1402021542 1402021534 |
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| 100 | 1 | |a Kantorovich, Lev |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Quantum theory of the solid state |b an introduction |c by Lev Kantorovich |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer Acad. Publ. |c 2004 | |
| 300 | |a XXV, 626 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Fundamental theories of physics |v 136 | |
| 650 | 4 | |a Physique de l'état solide | |
| 650 | 4 | |a Théorie quantique | |
| 650 | 4 | |a Quantentheorie | |
| 650 | 4 | |a Quantum theory | |
| 650 | 4 | |a Solid-state physics | |
| 650 | 0 | 7 | |a Quantentheorie |0 (DE-588)4047992-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Festkörper |0 (DE-588)4016918-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Festkörpertheorie |0 (DE-588)4154189-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Festkörperphysik |0 (DE-588)4016921-2 |2 gnd |9 rswk-swf |
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| 830 | 0 | |a Fundamental theories of physics |v 136 |w (DE-604)BV000012461 |9 136 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012794300&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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| adam_text | Contents
Acknowledgement
v
Foreword
vii
Introduction
ix
1
Structures
1
1.1
Crystals: periodic arrays of atoms
.................... 1
1.2
Mathematical description of crystal structures
.............. 4
1.2.1
Definition of a group
........................ 4
1.2.2
Translation groups
......................... 5
1.2.2.1
Operators of translation
.................
б
1.2.2.2
Construction of subgroups
............... 6
1.2.3
Point groups
............................ 7
1.2.3.1
Elementary point groups
................ 8
1.2.3.2
Symmetry groups of a tetrahedron and a cube
.... 10
1.2.4
Space groups
............................ 12
1.2.4.1
Symmetry operations
.................. 12
1.2.4.2
Types of
Bravais
lattices
................ 14
1.2.4.3
Crystallographic (conventional) unit cell
........ 19
1.2.4.4
Crystal classes
...................... 20
1.2.4.5
Symmorphic and nonsymmorphic crystal lattices
... 22
1.2.4.6
Close packing structures
................ 22
1.2.4.7
2D
(planai·)
groups
................... 23
1.2.5 *
Matrix and operator representations of a group
........ 23
1.2.5.1
Operator representation of a group
........... 23
1.2.5.2
Matrix representation of a group
............ 24
1.2.6
Indexing of planes and directions: definitions
.......... 25
1.3 *
International Tables for
Х
-Ray Crystallography
............ 26
1.4
Examples of crystal structures
....................... 30
1.4.1
Cubic face-centred structures
................... 31
1.4.1.1
Space group O))
(Frrúm,
No.
225)........... 31
1.4.1.2
Space group O7h (Fd3m, No.
227)........... 32
1.4.1.3
Space group T f,
(F43m, No.
216)........... 32
1.4.2
Cubic body-centred structures
.................. 32
1.4.2.1
Space group O9h
(Inani, No.
229)........... 32
XV
xvi CONTENTS
1.4.2.2 Space
group
T^
{lai, No.
206)............. 33
1.4.3
Structures with simple cubic lattice
............... 33
1.4.3.1
Space group
О^ (РтЗт,
No.
221)........... 33
1.4.3.2
Space group Tbh
(Pai, No.
205)............ 34
1.4.4
Tetragonal lattice
.......................... 34
1.4.4.1
Space group
Ό
(P^/mnm, No.
136)........ 34
1.4.5
Structures with trigonal lattice
.................. 35
1.4.5.1
Space group D|d
(Тс,
No.
167)............ 35
1.4.6
Structures with hexagonal lattice
................. 36
1.4.6.1
Space group Ojh
(Рб^/ттс,
No.
194)........ 36
1.4.6.2
Space group Cjv (P63mc, No.
186).......... 36
1.4.6.3
Space group D|
(РЗ121,
No.
152)........... 37
1.5
Nonperiodic solids
............................. 37
1.5.1
Definition of order and quasicrystals
............... 38
1.5.2
A road to disorder
......................... 40
1.5.2.1
Point defects
....................... 40
1.5.2.2
Cellular disorder
..................... 40
1.5.2.3
Topological disorder
................... 43
2
The reciprocal lattice and X-ray diffraction
45
2.1
The reciprocal lattice
............................ 45
2.2
*Once again about crystal planes and Miller indices
.......... 47
2.3
Brillouin zones
............................... 50
2.4
Periodic functions: Fourier analysis
.................... 51
2.5
Introduction to X-ray diffraction
..................... 55
2.5.1
Diffraction intensity
........................ 55
2.5.2
Bragg law
.............................. 59
2.5.3
Structure factor
........................... 60
2.5.4
Interpretation of diffraction experiments
............. 63
2.5.5 *
X-ray diffraction of nonperiodic solids
.............. 63
2.5.5.1
Density-density correlation function
.......... 64
2.5.5.2
Periodic systems revisited
................ 65
2.5.5.3
Application to a binary alloy
.............. 66
2.5.5.4
Glass
........................... 68
3
Binding in Crystals
69
3.1
Adiabatic approximation
......................... 69
3.2
Molecules: types of chemical bonding
................... 75
3.2.1
Simple example: a molecule with two atoms
........... 75
3.2.2
Ionic bond
.............................. 77
3.2.3
Covalent bond
........................... 77
3.2.3.1
Hydrogen molecular ion Hj
............... 77
3.2.3.2
Hydrogen molecule: MO method
............ 78
3.2.3.3
Hydrogen molecule: VB method
............ 82
3.2.3.4
Covalent bonds for elements having the (np)3 shells
. 83
3.2.3.5
Covalent bonds for elements having the (ns)2(np)2 shells
83
CONTENTS xvii
3.2.3.6
Some other examples of hybrid
orbitais
........ 84
3.2.4
Ion-Covalent bond
......................... 85
3.2.5
Van
der Waals
interaction
..................... 85
3.2.6
Hydrogen bond
........................... 88
3.3
Binding in crystals
............................. 88
3.3.1
Cohesive and lattice energies
................... 88
3.3.2
Electrostatic energy
........................ 89
3.3.2.1
Conditional convergence
................. 89
3.3.2.2
*Ewald method: electrostatic potential
........ 90
3.3.2.3
*Ewald constant
..................... 92
3.3.2.4
*Ewald method: electrostatic energy
.......... 93
3.3.2.5
The Madelung energy of a finite large crystal sample
94
3.3.3
Van
der Waals
crystals
....................... 94
3.3.4
Ionic crystals
............................ 95
3.3.5
Covalent crystals
.......................... 97
3.3.6
Hydrogen bond systems
...................... 98
3.3.7
Metals
................................ 98
3.3.8
Real crystals
............................ 99
4
Atomic vibrations
101
4.1
Lagrangian and Hamiltonian method
................... 101
4.2
One dimensional lattice
.......................... 103
4.2.1
Monoatomic basis
......................... 103
4.2.1.1
Lagrangian and equation of motion
.......... 104
4.2.1.2
General solution
..................... 105
4.2.1.3
First Brillouin zone
................... 106
4.2.1.4
Elastic Waves
...................... 106
4.2.1.5
Long wavelength limit
.................. 107
4.2.2
Two atoms in the basis
...................... 107
4.2.2.1
Lagrangian and equations of motion
.......... 108
4.2.2.2
Analysing the solution
.................. 109
4.2.2.3
Limiting case of identical atoms
............ 110
4.2.2.4
Why optical and acoustic?
............... 112
4.2.3
Boundary conditions
........................ 112
4.2.4
*Xormal coordinates
........................ 114
4.2.4.1
Discrete Fourier transform
............... 115
4.2.4.2
Matrix form for the eigenvalue problem and the dy¬
namical matrix of the chain
............... 116
4.2.4.3
Diagonal representation for the kinetic and potential
energies of the chain
.................. 118
4.2.4.4
Normal coordinates of the chain
............ 120
4.2.5
Density of states for the ID chain
................ 121
4.3
Three dimensional lattice: classical
.................... 122
4.3.1
Harmonic approximation
..................... 123
4.3.2
Phonons in a
3D
crystal
...................... 125
4.3.2.1
Hamiltonian and equations of motion
......... 125
xviii CONTENTS
4.3.2.2
Trial solution
....................... 125
4.3.2.3
Dynamical matrix
.................... 126
4.3.2.4
Eigenvalue and eigenvector problem for lattice vibrations
126
4.3.2.5
Symmetry properties
.................. 127
4.3.2.6
The
wavevector
..................... 128
4.3.2.7
General solution
..................... 129
4.3.3
Limiting case of long waves
.................... 129
4.3.3.1
Acoustic branches
.................... 130
4.3.3.2
Optical branches
..................... 130
4.3.4
Example: a crystal with central forces
.............. 131
4.3.4.1
Crystal with central forces
............... 131
4.3.4.2
Oscillations of a binary fee crystal
........... 133
4.3.5
Phonon density of states (DOS)
.................. 135
4.3.5.1
Contribution from long acoustic waves: Debye model
136
4.3.5.2
*Van Hove singularities
................. 137
4.3.6
*Normal coordinates
........................ 139
4.3.6.1 3D
discrete Fourier transform
.............. 139
4.3.6.2
Formal introduction of normal coordinates
...... 141
4.3.6.3
Diagonalisation of the kinetic and potential energies
using complex coordinates
............... 142
4.3.6.4
Introduction of real coordinates
............ 144
4.3.6.5
Lattice stability at zero temperature
.......... 145
4.4
Three dimensional lattice dynamics: quantum
.............. 145
4.4.1
A single harmonic oscillator
.................... 145
4.4.1.1
Introduction of creation and destruction (annihilation)
operators
......................... 146
4.4.1.2
Introduction to algebra of operators
α
and
α^
..... 147
4.4.1.3 *
Some useful operator identities
............ 149
4.4.2
Crystal vibrations in the harmonic approximation
....... 152
4.4.2.1
Second quantisation
................... 153
4.5
Thermal properties of crystals
....................... 155
4.5.1
Equilibrium statistical mechanics
................. 155
4.5.1.1
Classical statistical mechanics
............. 155
4.5.1.2
Quantum statistical mechanics
............. 156
4.5.2
Phonon statistics
.......................... 156
4.5.2.1
Phonons as quasiparticles
................ 158
4.5.2.2
*Some useful statistical averages
............ 158
4.5.2.3 *
Displacement-displacement correlation function
. . . 161
4.5.3
Internal energy and specific heat
................. 162
4.5.3.1
Internal energy
...................... 162
4.5.3.2
Specific heat
....................... 163
4.5.3.3
Debye model for acoustic branches
........... 163
4.5.3.4
Einstein model for optical branches
.......... 166
4.5.4
Equation of states
......................... 166
4.5.4.1
*Quasiharmonic approximation
............. 166
4.5.4.2
*Equation of state
.................... 168
CONTENTS xix
4.5.4.3
Thermal expansion
................... 169
4.5.5
Melting
............................... 170
4.5.6
Thermal
conductivity and anharmonicity
............ 172
4.5.6.1
Elementary kinetic theory of thermal conductivity
. . 172
4.5.6.2 *
Anharmonicity
..................... 173
4.5.7
*Debye-Waller factor
........................ 176
4.5.7.1
Elastic and inelastic phonon processes
......... 178
4.6
*Elementary theory of elasticity and stability
.............. 179
4.6.1
Main ideas of the classical theory of elasticity
.......... 179
4.6.1.1
External and Lagrangian strain
............. 180
4.6.1.2
Stress
........................... 182
4.6.1.3 Isotropie
pressure
.................... 184
4.6.1.4
Shear and normal strain and stress
........... 184
4.6.1.5
Thermodynamics
..................... 185
4.6.2
Elastic constants
.......................... 186
4.6.2.1
Elastic properties of crystals
.............. 186
4.6.2.2
Hooke s law
........................ 187
4.6.2.3
Crystal symmetry
.................... 187
4.6.2.4
Noncrystalline solids
................... 189
4.6.3
Stability
............................... 191
4.6.4
Elastic waves
............................ 193
4.6.4.1
Waves in a cubic crystal
................. 195
4.6.5
Method of homogeneous deformation
............... 196
4.6.5.1
General description of a homogeneous deformation in
a crystal
......................... 196
4.6.5.2
General expressions for the isothermal elastic constants
197
4.6.5.3
Example: a crystal with pairwise central interactions
200
5
Electrons in a periodic potential
203
5.1
Model of a free electron gas
........................ 203
5.1.0.4
Why electron gas?
.................... 203
5.1.1
Energies and wavefunctions
.................... 204
5.1.1.1
Periodic boundary conditions
.............. 204
5.1.1.2
Orthogonality and completeness of plane wa -es
.... 205
5.1.1.3
Distribution of electrons on energy levels. Fermi sphere
207
5.1.1.4
Density of states
..................... 208
5.1.2
Quantum statistics: Fermi-Dirac distribution
.......... 208
5.1.3
*Heat capacity and chemical potential of the electron gas
. . . 211
5.1.3.1
One useful integral
.................... 211
5.1.3.2
Chemical potential
.................... 212
5.1.3.3
Heat capacity
...................... 213
5.1.3.4
Comparison with experiment.
.............. 214
5.1.4
Transport processes
........................ 214
5.1.4.1
Electrical conductivity
.................. 215
5.1.4.2
Matthiessen s rule
.................... 215
5.1.4.3
Motion in magnetic field. Hall effect
.......... 216
xx CONTENTS
5.1.4.4
Thermal
conductivity
.................. 218
5.1.4.5
Wiedemann-Franz law
.................. 218
5.2
Energy bands
................................ 218
5.2.1
Bloch theorem
........................... 219
5.2.1.1
The meaning of vector
q
and periodic boundary con¬
ditions
.......................... 220
5.2.1.2
*Wannier functions
................... 221
5.2.2
Electronic band structure via plane waves
........... 222
5.2.2.1
*Density-functional theory and Kohn-Sham potential
223
5.2.2.2 *
Calculation of the
Hartree
potential
......... 225
5.2.3
Approximation of a nearly free electron gas
........... 227
5.2.3.1
Empty lattice approximation: reduced zone scheme
. 227
5.2.3.2
Model of a nearly free electron gas
........... 229
5.2.4
Tight binding method
....................... 231
5.2.4.1
An example:
s
bands
.................. 233
5.2.4.2
Assembling a crystal from atoms
............ 234
5.2.5
*Kronig-Penney model
....................... 234
5.2.6
Density of states (DOS)
...................... 236
5.2.7
Metals and insulators
....................... 239
5.3
Transport properties: electrical and thermal conductivity revisited
. . 242
5.3.1
Fermi surfaces
........................... 242
5.3.1.1
Examples
........................ 243
5.3.2
Quasiparticles
............................ 244
5.3.2.1
Particles and holes
.................... 244
5.3.2.2
Wave packets
....................... 245
5.3.3
Effective electron mass
....................... 248
5.3.4
Current in bands
.......................... 250
5.3.5
*Kinetic equation
.......................... 252
5.3.5.1
Collision term and the detailed balance
........ 254
5.3.5.2
Relaxation time approximation
............. 255
5.3.6
*Electrical conductivity
...................... 256
5.3.7
*Heat transport
........................... 258
5.3.8 *
Quantum description of transport processes
.......... 259
5.3.8.1
Nonequilibrium quantum statistical mechanics
.... 259
5.3.8.2
Kubo s linear response theory
............. 261
5.3.8.3
Generalised susceptibilities
............... 263
5.3.8.4
General expression for electrical conductivity
..... 264
5.3.8.5
Relaxation time approximation
............. 265
5.4
Electron-electron interaction
........................ 266
5.4.1
Qualitative consideration
..................... 266
5.4.2
*Elementary theory of plasma oscillations
........... 268
5.4.2.1
Excitations of plasmons by fast electrons
....... 270
5.4.2.2
Interaction with electromagnetic waves
........ 271
5.4.2.3
Interaction with longitudinal electrostatic field
.... 273
5.4.3
Theory of plasma oscillations based on density fluctuations
. . 274
5.4.3.1
Electron Hamiltonian in the jellium model
...... 274
CONTENTS xxi
5.4.3.2
Classical treatment of plasma oscillations
....... 276
5.4.3.3
Quantum treatment of plasma oscillations
....... 278
5.4.4
*Screening in the electron gas
................... 279
5.4.4.1
Screening Coulomb potential of a point charge
.... 280
5.4.5
*Dielectric function of the electron gas
.............. 283
5.4.5.1
Maxwell equations for zero magnetic field
....... 284
5.4.5.2
Tensor of the microscopic dielectric function
..... 285
5.4.5.3
General expression for electronic susceptibility
.... 288
5.4.5.4
Self-consistent consideration of the electronic response
290
5.4.5.5
Susceptibility in the independent particles approxima¬
tion
............................ 291
5.4.5.6
Application to a free electron gas
............ 294
6
Magnetism
299
6.1
Magnetic moment in classical electrodynamics
.............. 299
6.1.1
Magnetic field of a system of moving charges far away from them.299
6.1.1.1
Relation between the magnetic moment and angular
momentum
........................ 301
6.1.2
Movement of a charged particle in a magnetic field
....... 301
6.1.3
Magnetic field in matter and magnetic permeability
...... 303
6.2
Magnetic moment in quantum mechanics
................ 307
6.2.1
*Relativistic description of an electron
.............. 307
6.2.1.1
Dirac equation
...................... 307
6.2.1.2
Solution of the Dirac equation for a free relativistic
electron
.......................... 309
6.2.1.3
Spin
............................ 310
6.2.2
*An electron in electro-magnetic field
.............. 312
6.2.2.1
Magnetic moment of an electron
............ 314
6.2.2.2
Quasi-relativistic approach
............... 314
6.2.2.3
An electron in a magnetic field
............. 315
6.2.3
*One electron atom in a homogeneous magnetic field
...... 316
6.2.4
Magnetic moment of an atom
.................. 317
6.2.4.1
One electron atom (ion)
................. 317
6.2.4.2
Alany-electron atom (ion)
................ 319
6.2.4.3 Hund
rules and physical reasons for permanent lo¬
calised magnetic moments
................ 320
6.3
Thermodynamics of magnetic materials
................. 321
6.4
Para- and diamagnetism of localised electrons
.............. 322
6.4.1
Classical paradox
.......................... 322
6.4.2
Almost classical theory of diamagnetism
............. 32.3
6.4.3
Quantum theory of diamagnetism
................ 324
6.4.4
Almost classical theory of paramagnetism
(Langevin)
..... 325
6.4.5
Quantum theory of paramagnetism
................ 327
6.5
Para- and diamagnetism of the electron gas
............... 329
6.5.1 Pauli
paramagnetism
....................... 329
XXII
CONTENTS
6.5.2
*Magnetism
of electrons in metals: Landau diamagnetism and
the
de Haas-van Alphen
effect
................... 331
6.5.2.1
General expression for the grand potential
...... 331
6.5.2.2 Pauli
paramagnetism versus Landau diamagnetism
. 335
6.5.2.3
The
de Haas-van Alphen
effect
............. 336
6.6
Magnetic ordering
.............................336
6.6.1
Interaction between localised magnetic moments
........336
6.6.1.1
Weiss molecular field
.................. 336
6.6.1.2
Curie-Weiss law
..................... 337
6.6.1.3
Ferromagnetism
..................... 338
6.6.1.4
Antiferromagnetism
................... 339
6.6.1.5
Ferrimagnetism
..................... 342
6.6.2
Hysteresis and domain structure
................. 343
6.6.2.1
Hysteresis curve
..................... 343
6.6.2.2
Anisotropy
........................ 344
6.6.2.3
Domains
......................... 344
6.6.2.4
Wall motion and rotation versus reversibility and ir-
reversibility
........................ 346
6.6.2.5
Domain energetics
.................... 346
6.6.3
Exchange interaction and the phenomenological theory of fer¬
romagnetism
............................ 347
6.6.3.1
Hydrogen molecule revisited
.............. 348
6.6.3.2
*Spin Hamiltonians
................... 349
6.6.3.3 *
Indirect exchange
................... 350
6.6.3.4
*Mean field method
................... 351
6.6.4
*Band theory of ferromagnetism
................. 352
6.6.4.1
Exchange interaction in metals: exchange hole
.... 352
6.6.4.2
Stoner
model: general equations
............ 353
6.6.4.3
Stoner
model: paramagnetism
............. 355
6.6.4.4
Stoner
model: ferromagnetism
............. 356
6.6.4.5
Stoner
model: specific heat
............... 357
6.7
Symmetry breaking and order parameters
................ 357
6.7.1
Symmetry breaking
........................358
6.7.2
The Landau theory of second order phase transition
......360
6.7.3
*Bragg-Williams theory
......................362
Superconductivity
367
7.1
General properties
............................. 367
7.1.1
Critical magnetic field and critical current
............ 368
7.1.2
Meissner-Ochsenfeld effect
..................... 368
7.1.2.1
Superconducting phase transition
........... 370
7.1.2.2
Heat capacity
...................... 370
7.1.2.3
Isotope effect
....................... 371
7.2
Phenomenological theory of superconductivity
.............. 371
7.2.1
Thermodynamics of superconductors
............... 371
7.2.2
London equations
.......................... 373
CONTENTS xxiü
7.2.2.1
Expérimental
evidence
................. 376
7.3 Main
ideas of the microscopic theory of superconductivity
....... 377
7.3.1
Attraction between electrons
................... 377
7.3.2
Cooper pairs
............................ 379
7.3.3
*Ground state of the metal in the superconducting state
.... 382
7.3.3.1
Creation and annihilation operators for electrons in a
normal metal
....................... 382
7.3.3.2
Variational wavefunction for a superconductor
.... 384
7.3.3.3
Calculation of the ground state using a variational
method
.......................... 386
7.3.3.4
Isotope effect
....................... 391
7.3.3.5
Correlation and coherence lengths
........... 391
7.3.4
*Excitation energies in the superconducting state
....... 393
7.3.4.1
Energy gap
........................ 397
7.3.4.2
Temperature dependence
................ 399
7.3.5
Supercurrents
............................ 401
7.3.6
Existence of the critical magnetic field
.............. 403
7.3.7
*The Meissner-Ochsenfeld effect
................. 404
7.3.7.1
Current density operator
................ 404
7.3.7.2
Coordinate representation of the wave function
. . . 405
7.3.7.3
Derivation of the second London equation
....... 406
7.3.8
Quantisation of magnetic flux
................... 407
7.4
*Ginzburg-Landau theory of superconductivity
............. 409
7.4.1
Order parameter and the free energy
............... 410
7.4.2
Ginzburg-Landau equations
.................... 412
7.4.3
Examples of applications
..................... 414
7.5
Type II superconductors
.......................... 415
7.6
High Tc superconductors
.......................... 416
7.6.0.1
Cuprates
......................... 416
7.6.0.2
Fullerenes
......................... 419
8
Dielectric materials
421
8.1
Microscopic polarisation
.......................... 422
8.2
Phonon contribution to the dielectric function
.............. 426
8.2.1
The local field
........................... 426
8.2.2
Optical vibrations of a binary ionic crystal
........... 429
8.2.2.1
Huang equations
..................... 430
8.2.2.2
Dispersion formula for the dielectric function
..... 434
8.2.2.3
Long optical phonons
.................. 436
8.2.3
*General consideration: classical
................. 438
8.2.4
*General consideration: quantum
................ 443
8.3
Thermodynamics of dielectrics
...................... 447
8.3.1
Contribution of the field to thermodynamic potentials
..... 447
8.3.1.1 Isotropie
dielectrics
................... 448
8.3.1.2
Crystals
.......................... 448
8.3.1.3
*Pyroelectrics and crystal symmetry
.......... 449
xxiv CONTENTS
8.3.1.4
Dielectric tensor and crystal symmetry
........ 449
8.3.2
*Effect of the elastic deformation
................. 450
8.3.2.1
Piezoelectric tensor
................... 451
8.3.2.2
Crystal symmetry allowing piezoelectricity
...... 452
8.3.2.3
Statics and dynamics of a piezoelectric crystal
.... 453
8.3.2.4
Elastic waves in piezoelectrics
............. 454
8.4
Ferroelectric transition
........................... 455
8.4.1
General description of ferroelectrics
............... 455
8.4.2
Landau theory of the ferroelectric phase transition
....... 460
8.4.2.1
Second order transition
................. 461
8.4.2.2
First order transitions
.................. 462
8.4.3
*Microscopic consideration: Effective field model of Lines
. . . 465
9
Modern methods
of electronic structure calculations
471
9.1
Many-electron wavefunction
........................ 472
9.1.1
Antisymmetry
........................... 472
9.1.2
Slater determinants
........................ 474
9.1.2.1
Antisymmetriser
..................... 477
9.1.2.2
Creation and annihilation operators
.......... 478
9.1.3
Slater rules: matrix elements between determinants
...... 480
9.1.3.1
Non-orthogonal spin-orbitals
.............. 484
9.1.4
Operators in second quantisation
................. 484
9.1.4.1
One-particle operator
.................. 485
9.1.4.2
Two-particle operator
.................. 487
9.1.4.3
Total energy
....................... 488
9.1.5
Reduced density matrices
..................... 488
9.1.5.1
Electron densities
.................... 488
9.1.5.2
Reduced density matrices
................ 490
9.1.5.3
Natural
orbitais
and occupation numbers
....... 492
9.2
Quantum chemistry methods
....................... 493
9.2.1
Configuration Interaction
(CI)
method
.............. 494
9.2.2
Variational calculus
........................ 496
9.2.3
Hartree-Fock theory
........................ 499
9.2.3.1
Hartree-Fock energy and electronic density
...... 501
9.2.3.2
Variational method: Hartree-Fock equations
..... 502
9.2.3.3
Koopman s theorem and physical significance of
e¿
. . 506
9.2.3.4
Closed shell electron system
.............. 507
9.2.3.5
Hartree-Fock-Roothaan method
............ 508
9.2.4
HF theory of the homogeneous electron gas
........... 510
9.2.5
Electronic correlation
....................... 514
9.3
Density Functional Theory
........................ 518
9.3.1
Hohenberg-Kohn theorems
.................... 518
9.3.2
The Levy constrained search method
............... 521
9.3.3
The Kohn-Sham method
...................... 523
9.3.3.1
Relation to a fictitious noninteracting electron gas
. . 523
CONTENTS xxv
9.3.3.2
Derivation of the KS equations from the variational
principle
......................... 524
9.3.3.3
Matrix form of the KS equations
............ 526
9.3.3.4
Local density approximation (LDA) and beyond
. . . 527
9.3.3.5
More about the KS equations
.............. 530
9.3.3.6
Meaning of the KS eigenvalues
............. 531
9.3.4
Spin polarised DFT
........................ 533
9.3.5
Other extensions of the DFT
...................
53G
9.3.5.1
Excited states
...................... 536
9.3.5.2
Nonzero temperatures
.................. 537
9.3.5.3
Time dependent DFT (TDDFT)
............ 538
9.4
Some technical details
........................... 539
9.4.1
Basis set
............................... 539
9.4.2
Periodic boundary conditions and k-point sampling
...... 542
9.4.3
Pseudopotentials: hard and soft
................ 546
9.4.4
Exact pseudopotentials: PAW method
............. 551
9.4.5
Order-N methods
.......................... 552
9.5 Ab initio
simulations
............................ 553
9.5.1
Static properties: energies and forces
.............. 554
9.5.1.1
Hellmann-Feynman theorem
.............. 555
9.5.1.2
Pulay forces
....................... 557
9.5.1.3
Stress
........................... 559
9.5.1.4
Electronic DOS
..................... 560
9.5.1.5
Adsorption of atomic and molecular oxygen on the
MgO
(001)
surface
.................... 561
9.5.2 Ab
initio molecular dynamics simulations
............ 568
9.5.2.1
Hydrolysis at stepped MgO surfaces
.......... 571
9.5.2.2
Calculation of free energies
............... 573
9.5.3 Ab
initio lattice dynamics: direct method
............ 576
9.5.4
Density functional perturbation theory
............. 580
9.5.5
Quantum polarisation
....................... 585
Bibliography
595
Index
609
|
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| author | Kantorovich, Lev |
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| dewey-sort | 3530.4 11 |
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| id | DE-604.BV019327291 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:57:45Z |
| institution | BVB |
| isbn | 1402018215 1402021542 1402021534 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012794300 |
| oclc_num | 53954293 |
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| owner_facet | DE-703 DE-20 DE-355 DE-BY-UBR DE-29T DE-11 |
| physical | XXV, 626 S. Ill., graph. Darst. |
| publishDate | 2004 |
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| publisher | Kluwer Acad. Publ. |
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| series | Fundamental theories of physics |
| series2 | Fundamental theories of physics |
| spelling | Kantorovich, Lev Verfasser aut Quantum theory of the solid state an introduction by Lev Kantorovich Dordrecht [u.a.] Kluwer Acad. Publ. 2004 XXV, 626 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Fundamental theories of physics 136 Physique de l'état solide Théorie quantique Quantentheorie Quantum theory Solid-state physics Quantentheorie (DE-588)4047992-4 gnd rswk-swf Festkörper (DE-588)4016918-2 gnd rswk-swf Festkörpertheorie (DE-588)4154189-3 gnd rswk-swf Festkörperphysik (DE-588)4016921-2 gnd rswk-swf Quantentheorie (DE-588)4047992-4 s Festkörper (DE-588)4016918-2 s DE-604 Festkörpertheorie (DE-588)4154189-3 s Festkörperphysik (DE-588)4016921-2 s Fundamental theories of physics 136 (DE-604)BV000012461 136 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012794300&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kantorovich, Lev Quantum theory of the solid state an introduction Fundamental theories of physics Physique de l'état solide Théorie quantique Quantentheorie Quantum theory Solid-state physics Quantentheorie (DE-588)4047992-4 gnd Festkörper (DE-588)4016918-2 gnd Festkörpertheorie (DE-588)4154189-3 gnd Festkörperphysik (DE-588)4016921-2 gnd |
| subject_GND | (DE-588)4047992-4 (DE-588)4016918-2 (DE-588)4154189-3 (DE-588)4016921-2 |
| title | Quantum theory of the solid state an introduction |
| title_auth | Quantum theory of the solid state an introduction |
| title_exact_search | Quantum theory of the solid state an introduction |
| title_full | Quantum theory of the solid state an introduction by Lev Kantorovich |
| title_fullStr | Quantum theory of the solid state an introduction by Lev Kantorovich |
| title_full_unstemmed | Quantum theory of the solid state an introduction by Lev Kantorovich |
| title_short | Quantum theory of the solid state |
| title_sort | quantum theory of the solid state an introduction |
| title_sub | an introduction |
| topic | Physique de l'état solide Théorie quantique Quantentheorie Quantum theory Solid-state physics Quantentheorie (DE-588)4047992-4 gnd Festkörper (DE-588)4016918-2 gnd Festkörpertheorie (DE-588)4154189-3 gnd Festkörperphysik (DE-588)4016921-2 gnd |
| topic_facet | Physique de l'état solide Théorie quantique Quantentheorie Quantum theory Solid-state physics Festkörper Festkörpertheorie Festkörperphysik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012794300&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000012461 |
| work_keys_str_mv | AT kantorovichlev quantumtheoryofthesolidstateanintroduction |