目錄
Preface to the second edition
Preface to the first edition
1 Electrons in One-Dimensional Periodic Potentials
1.1 The Bloch Theorem for One-Dimensional Periodicity
1.2 Energy Levels of a Single Quantum Well and of a Periodic Array of Quantum Wells
1.3 Transfer Matrix, Resonant Tunneling, and Energy Bands
1.4 The Tight-Binding Model
1.5 Plane Waves and Nearly Free-Electron Model
1.6 Some Dynamical Aspects of Electrons in Band Theory
Appendix A. Solved Problems and Complements
Further Reading
2 Geometrical Description of Crystals: Direct and Reciprocal Lattices
2.1 Simple Lattices and Composite Lattices
2.2 Geometrical Description of Some Crystal Structures
2.3 Wigner-Seitz Primitive Cells
2.4 Reciprocal Lattices
2.5 Brillouin Zones
2.6 Translational Symmetry and Quantum Mechanical Aspects
2.7 Density-of-States and Critical Points
Further Reading
3 The Sommerfeld Free-Electron Theory of Metals
3.1 Quantum Theory of the Free-Electron Gas
3.2 Fermi-Dirac Distribution Function and Chemical Potential
3.3 Electronic Specific Heat in Metals and Thermodynamic Functions
3.4 Thermionic Emission from Metals
Appendix A. Outline of Statistical Physics and Thermodynamic Relations
Appendix B. Fermi-Dirac and Bose-Einstein Statistics for Independent Particles
Appendix C. Modified Fermi-Dirac Statistics in a Model of Correlation Effects
Further Reading
4 The One-Electron Approximation and Beyond
4.1 Introductory Remarks on the Many-Electron Problem
4.2 The Hartree Equations
4.3 Identical Particles and Determinantal Wavefunctions
4.4 Matrix Elements Between Determinantal States
4.5 The Hartree-Fock Equations
4.6 Overview of Approaches Beyond the One-Electron Approximation
4.7 Electronic Properties and Phase Diagram of the Homogeneous Electron Gas
4.8 The Density Functional Theory and the Kohn-Sham Equations
Appendix A. Bielectronic Integrals Among Spin Orbitals
Appendix B. Outline of Second Quantization Formalism for Identical Fermions
Appendix C. An Integral on the Fermi Sphere
Further Reading
5 Band Theory of Crystals
5.1 Basic Assumptions of the Band Theory
5.2 The Tight-Binding Method (LCAO Method)
5.3 The Orthogonalized Plane Wave (OPW) Method
5.4 The Pseudopotential Method
5.5 The Cellular Method
5.6 The Augmented Plane Wave (APW) Method
5.7 The Green's Function Method (KKR Method)
5.8 Iterative Methods in Electronic Structure Calculations
Appendix A. Matrix Elements of the Augmented Plane Wave Method
Appendix B. Solved Problems and Complements
Appendix C. Evaluation of the Structure Coefficients of the KKR Method with the Ewald Procedure
Further Reading
6 Electronic Properties of Selected Crystals
6.1 Band Structure and Cohesive Energy of Rare-Gas Solids
6.2 Electronic Properties of Ionic Crystals
6.3 Covalent Crystals with Diamond Structure
6.4 Band Structures and Fermi Surfaces of Some Metals
6.5 Carbon-Based Materials and Electronic Structure of Graphene
Appendix A. Solved Problems and Complements
Further Reading
7 Excitons, Plasmons, and Dielectric Screening in Crystals
7.1 Exciton States in Crystals
7.2 Plasmon Excitations in Crystals
7.3 Static Dielectric Screening in Metals within the Thomas-Fermi Model
7.4 The Longitudinal Dielectric Function within the Linear Response Theory
7.5 Dielectric Screening within the Lindhard Model
7.6 Quantum Expression of the Longitudinal Dielectric Function in Crystals
7.7 Surface Plasmons and Surface Polaritons
Appendix A. Friedel Sum Rule and Fumi Theorem
Appendix B. Quantum Expression of the Longitudinal Dielectric Function in Materials with the Linear Response Theory
Appendix C. Lindhard Dielectric Function for the Free-Electron Gas
Appendix D. Quantum Expression of the Transverse Dielectric Function in Materials with the Linear Response Theory
Further Reading
8 Interacting Electronic-Nuclear Systems and the Adiabatic Principle
8.1 Interacting Electronic-Nuclear Systems and Adiabatic Potential-Energy Surfaces
8.2 Non-Degenerate Adiabatic Surface and Nuclear Dynamics
8.3 Degenerate Adiabatic Surfaces and Jahn-Teller Systems
8.4 The Hellmann-Feynman Theorem and Electronic-Nuclear Systems
8.5 Parametric Hamiltonians and Berry Phase
8.6 The Berry Phase Theory of the Macroscopic Electric Polarization in Crystals
Appendix A. Simplified Evaluation of Typical Jahn-Teller and Rermer-Teller Matrices
Appendix B. Solved Problems and Complements
Further Reading
9 Lattice Dynamics of Crystals
9.1 Dynamics of Monoatomic One-Dimensional Lattices
9.2 Dynamics of Diatomic One-Dimensional Lattices
9.3 Dynamics of General Three-Dimensional Crystals
9.4 Quantum Theory of the Harmonic Crystal
9.5 Lattice Heat Capacity. Einstein and Debye Models
9.6 Considerations on Anharmonic Effects and Melting of Solids
9.7 Optical Phonons and Polaritons in Polar Crystals
Appendix A. Quantum Theory of the Linear Harmonic Oscillator
Further Reading
10 Scattering of Particles by Crystals
10.1 General Considerations
10.2 Elastic Scattering of X-rays from Crystals and the Thomson Approximation
10.3 Compton Scattering and Electron Momentum Density
10.4 Inelastic Scattering of Particles and Phonons Spectra of Crystals
10.5 Quantum Theory of Elastic and Inelastic Scattering of Neutrons
10.6 Dynamical Structure Factor for Harmonic Displacements and Debye-Waller Factor
10.7 M0ssbauer Effect
Appendix A. Solved Problems and Complements
Further Reading
11 Optical and Transport Properties of Metals
11.1 Macroscopic Theory of Optical Constants in Homogeneous Materials
11.2 The Drude Theory of the Optical Properties of Free Carriers
11.3 Transport Properties and Boltzmann Equation
11.4 Static and Dynamic Conductivity in Metals
11.5 Boltzmann Treatment and Quantum Treatment of lntraband Transitions
11.6 The Boltzmann Equation in Electric Fields and Temperature Gradients
Appendix A. Solved Problems and Complements
Further Reading
12 Optical Properties of Semiconductors and Insulators
12.1 Transverse Dielectric Function and Optical Constants in Homogeneous Media
12.2 Quantum Theory of Band-to-Band Optical Transitions and Critical Points
12.3 Indirect Phonon-Assisted Transitions
12.4 Two-Photon Absorption
12.5 Exciton Effects on the Optical Properties
12.6 Fano Resonances and Absorption Lineshapes
12.7 Optical Properties of Vibronic Systems
Appendix A. Transitions Rates at First and Higher Orders of Perturbation Theory
Appendix B. Optical Constants, Green's Function and Kubo-Greenwood Relation
Further Reading
13 Transport in Intrinsic and Homogeneously Doped Semiconductors
13.1 Fermi Level and Carrier Density in Intrinsic Semiconductors
13.2 Impurity Levels in Semiconductors
13.3 Fermi Level and Carder Density in Doped Semiconductors
13.4 Non.Equilibrium Carrier Distributions
13.5 Generation and Recombination of Electron-Hole Pairs in Doped Semiconductors
Appendix A. Solutions of Typical Transport Equations in Uniformly Doped Semiconductors
Further Reading
14 Transport in Inhomogeneous Semiconductors
14.1 Properties of the p-n Junction at Equilibrium
14.2 Current-Voltage Characteristics of the p-n Junction
14.3 The Bipolar Junction Transistor
14.4 Semiconductor Heterojunctions
14.5 Metal-Semiconductor Contacts
14.6 Metal-Oxide-Semiconductor Structure
14.7 Metal-Oxide-Semiconductor Field-Effect Transistor (MOSFET)
Further Reading
15 Electron Gas in Magnetic Fields
15.1 Magnetization and Magnetic Susceptibility
15.2 Energy Levels and Density-of-States of a Free Electron Gas in Magnetic Fields
15.3 Landau Diamagnetism and de Haas-van Alphen Effect
15.4 Spin Paramagnetism of a Free-Electron Gas
15.5 Magnetoresistivity and Classical Hall Effect
15.6 Quantum Hall Effects
Appendix A. Solved Problems and Complements
Further Reading
16 Magnetic Properties of Localized Systems and Kondo Impurities
16.1 Quantum Mechanical Treatment of Magnetic Susceptibility
16.2 Permanent Magnetic Dipoles in Atoms or Ions with Partially Filled Shells
16.3 Paramagnetism of Localized Magnetic Moments
16.4 Localized Magnetic States in Normal Metals
16.5 Dilute Magnetic Alloys and the Resistance Minimum Phenomenon
16.6 Magnetic Impurity in Normal Metals at Very Low Temperatures
Further Reading
17 Magnetic Ordering in Crystals
17.1 Ferromagnetism and the Weiss Molecular Field
17.2 Microscopic Origin of the Coupling Between Localized Magnetic Moments
17.3 Antiferromagnetism in the Mean Field Approximation
17.4 Spin Waves and Magnons in Ferromagnetic Crystals
17.5 The lsing Model with the Transfer Matrix Method
17.6 The Ising Model with the Renormalization Group Theory
17.7 Itinerant Magnetism
Appendix A. Solved Problems and Complements
Further Reading
18 Superconductivity
18.1 Some Phenomenological Aspects of Superconductors
18.2 The Cooper Pair Idea
18.3 Ground State for a Superconductor in the BCS Theory at Zero Temperature
18.4 Excited States of Superconductors at Zero Temperature
18.5 Treatment of Superconductors at Finite Temperature and Heat Capacity
18.6 The Phenomenological London Model for Superconductors
18.7 Macroscopic Quantum Phenomena
18.8 Tunneling Effects
Appendix A. The Phonon-lnduced Electron-Electron Interaction
Further Reading
Index
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