Solid State Theory, Volume 1: Basics: Phonons and Electrons in Crystals

✍ Scribed by Gerd Czycholl

• Publisher: Springer
• Year: 2023
• Tongue: English
• Leaves: 407
• Category: Library

✦ Synopsis

The textbooks “Solid State Theory" give an introduction to the methods, contents and results of modern solid state physics in two volumes. This first volume has the basic courses in theoretical physics as prerequisites, i.e. knowledge of classical mechanics, electrodynamics and, in particular, quantum mechanics and statistical physics is assumed. The formalism of second quantization (occupation number representation), which is needed for the treatment of many-body effects, is introduced and used in the book. The content of the first volume deals with the classical areas of solid state physics (phonons and electrons in the periodic potential, Bloch theorem, Hartree-Fock approximation, density functional theory, electron-phonon interaction). The first volume is already suitable for Bachelor students who want to go beyond the basic courses in theoretical physics and get already familiar with an application area of theoretical physics, e.g. for an elective subject "Theoretical (Solid State) Physics" or as a basis for a Bachelor thesis. Every solid-state physicist working experimentally should also be familiar with the theoretical methods covered in the first volume. The content of the first volume can therefore also be the basis for a module "Solid State Physics" in the Master program in Physics or, together with the content of the 2nd volume, for a module "Theoretical Solid State Physics" or "Advanced Theoretical Physics". The following second volume covers application areas such as superconductivity and magnetism to areas that are current research topics (e.g. quantum Hall effect, high-temperature superconductivity, low-dimensional structures).

✦ Table of Contents

Preface to the Fourth (German) Edition
Extract from the Preface to the First German Edition
Contents
1 Introduction
2 Periodic Structures
2.1 Crystal Structure, Bravais Lattice, Wigner-Seitz Cell
2.1.1 Crystallization of Solids
2.1.2 Crystal System and Crystal Lattice
2.1.3 Symmetry Group of the Crystal Systems
2.1.4 Bravais Lattice, Primitive Unit Cell and Wigner-Seitz Cell
2.1.5 Crystal Structures
2.2 The Reciprocal Lattice, Brillouin Zone
2.3 Periodic Functions
2.4 Problems for Chap. 2
3 Separation of Lattice and Electron Dynamics
3.1 The General Solid-State Hamiltonian Operator
3.2 Adiabatic Approximation (Born-Oppenheimer Approximation)
3.3 Bonding and Effective Nuclear-Nuclear Interaction
3.4 Problems for Chap. 3
4 Lattice Vibrations (Phonons)
4.1 Harmonic Approximation, Dynamic Matrix and Normal Coordinates
4.2 Classical Equations of Motion
4.3 Periodic or Born-von-Kármán Boundary Conditions
4.4 Quantized Lattice Vibrations and Phonon Dispersion Relations
4.5 Thermodynamics of Lattice Vibrations (Phonons), Debye and Einstein Model
4.6 Phonon Spectra and Densities of States
4.6.1 Example: Simple Cubic Lattice
4.6.2 Phonon Density of States
4.7 Long Wavelength Limit
4.7.1 Acoustic phonons and elastic waves
4.7.2 Long Wavelength Optical Phonons and Electromagnetic Waves, Polaritons
4.8 (Neutron) Scattering on Crystals (Phonons), Debye-Waller Factor
4.9 Anharmonic Corrections
4.10 Problems for Chap. 4
5 Non-interacting Electrons in the Solid State
5.1 Electron in periodic potential, Bloch theorem
5.2 Nearly Free Electron Approximation
5.3 Effective mass tensor, group velocity and k · p-perturbation theory
5.4 Tight binding model, Wannier states
5.5 Basic ideas of numerical methods for calculating the electronic band structure
5.5.1 Cellular method
5.5.2 Expansion in plane waves
5.5.3 APW-(“Augmented Plane Waves”)-Method
5.5.4 Green function method by Korringa, Kohn and Rostoker, KKR method
5.5.5 OPW-(“orthogonalized plane waves”)-method
5.5.6 Pseudopotential method
5.6 Electronic classification of solids
5.7 Electronic density of states and Fermi surface
5.8 Quantum statistics and thermodynamics of solid-state electrons
5.9 Statistics of electrons and holes in semiconductors
5.10 Problems for Chapter 5
6 Electron–Electron Interaction
6.1 Occupation Number Representation (“Second Quantization”) for Fermions
6.2 Models of Interacting Electron Systems in Solid State Physics
6.3 Hartree-Fock Approximation
6.3.1 Derivation from the Ritz Variation Principle
6.3.2 Derivation from a Variational Principle for the Grand Canonical Potential
6.4 Homogeneous Electron Gas in Hartree-Fock Approximation
6.5 Basic Ideas of Density Functional Theory
6.6 Elementary Theory of Static Screening
6.6.1 Thomas-Fermi Theory of Screening
6.6.2 Lindhard Theory of Screening
6.6.3 Static Screening in Semiconductors
6.7 Excitations in the Homogeneous Electron Gas, Plasmons
6.8 Excitons in Semiconductors
6.9 Quasiparticles and Landau Theory of the Fermi Liquid
6.10 Problems for Chap. 6
7 Electron-phonon Interaction
7.1 Hamiltonian of the Electron-Phonon Interaction
7.2 Renormalization of the Effective Electron Mass
7.3 Screening Effects on Phonon Dispersion and Electron-Phonon Interaction
7.4 Electron-Phonon Interaction in Ionic Crystals
7.5 The Polaron
7.6 Problems for Chap. 7
8 Solutions to the Exercise Problems
8.1 Solution of the Problems for Chap. 2
8.2 Solution to Exercise Problems for Chap. 3
8.3 Solution of the Exercise Problems for Chap. 4
8.4 Solution of the Problems for Chap. 5
8.5 Solution to the Problems of Chap. 6
8.6 Solution to Problems in Chap. 7
References