Quantum Solid-State Physics

ISBN-13: 9783642501661 / Angielski / Miękka / 2012 / 505 str.

Serghey V. Vonsovsky;Mikhail I. Katsnelson

Opis

This book treats the major problems of the quantum physics of solids, ranging from fundamental concepts to topical issues. Rather than use a deductive method of exposition, the authors consider and analyze simple empirically established properties of solids and employ more complicated models only as the need arises. Detailed treatment is given of classical problems such as chemical bonding in crystals, the one-dimensional Schrodinger equation with a periodic potential, the metal-insulator criterion, and the quantum theory of band electron motion in external fields. Consideration is also given to topical problems such as neutron scattering by the crystal lattice, plasma and Fermi liquid effects, the theory of disordered systems, and the polaron. The reader is expected to know only the fundamentals of quantum mechanics and statistical physics. Compared with the Russian edition (Nauka, Moscow 1983), the book has been substantially revised and enlarged, new sections have been written and recent results have been incorporated."

Spis treści

1. Introduction. General Properties of the Solid State of Matter.- 1.1 General Thermodynamic Description of the Solid State.- 1.2 Crystal Structure of Solids.- 1.3 Reciprocal Lattice.- 1.4 Examples of Simple Crystal Structures.- 1.5 Experimental Techniques for Determining the Periodic Atomic Structure of Solids.- 1.6 Qualitative Concepts of the Electronic and Nuclear Crystal Structure.- 1.7 Fundamental Concepts of the Chemical Bonding in Solids.- 1.7.1 Interaction Between Atoms (Ions) with Filled Electron Shells.- 1.7.2 Molecular Orbitals.- 1.7.3 The Heitler-London Method.- 1.7.4 Covalent Bond.- 1.7.5 Electrostatic Bonding Energy of Ionic Crystals.- 1.8 Types of Crystalline Solids.- 1.8.1 Ionic Crystals.- 1.8.2 Covalent Crystals and Semiconductors.- 1.8.3 Metals, Their Alloys, and Compounds.- 1.8.4 Molecular Crystals.- 1.8.5 Hydrogen-Bonded Crystals.- 1.8.6 Quasi-One-Dimensional and Quasi-Two-Dimensional Crystals.- 1.8.7 Quantum Crystals.- 1.9 Formulation of the General Quantum-Mechanical Problem of the Crystal.- 1.10 Properties of Disordered Condensed Systems.- 1.10.1 General Remarks.- 1.10.2 Metallic Glasses (Example of Amorphous Solids).- 2. Dynamic Properties of the Crystal Lattice.- 2.1 The Dynamics of the Ionic Lattice.- 2.1.1 A Linear Monatomic Array.- 2.1.2 A Linear Diatomic Array.- 2.1.3 The Three-Dimensional Crystal Case.- 2.1.4 Quantization of Ionic-Lattice Vibrations.- 2.2 The Specific-Heat Capacity of the Lattice.- 2.3 Allowance for Anharmonic Terms.- 2.3.1 Thermal Expansion of Crystals.- 2.3.2 Heat-Capacity Term Linear in Temperature.- 2.3.3 Thermal Conductivity of an Ionic Lattice.- 2.4 Localization of Phonons on Point Defects.- 2.5 Heat Capacity of Glasses at Low Temperatures.- 2.6 High-Frequency Permittivity of Ionic Crystals.- 2.7 Lattice Scattering and the Mössbauer Effect.- 2.7.1 Scattering Probability and the Correlation Function.- 2.7.2 Some Properties of the Phonon Operators and of the Averages Containing Them.- 2.7.3 Calculating the Dynamic Form Factor in the Harmonic Approximation.- 2.7.4 Elastic Scattering.- 2.7.5 Inelastic Scattering.- 2.7.6 The Mössbauer Effect.- 2.8 Conclusion.- 3. Simple Metals: The Free Electron-Gas Model.- 3.1 Types of Metals.- 3.2 Physical Properties of the Metallic State. Conduction Electrons.- 3.3 Classical Conduction-Electron Theory (Drude-Lorentz Theory).- 3.4 Itinerant Electron Theory According to Frenkel.- 3.5 Application of Fermi-Dirac Quantum Statistics to the Conduction-Electron Gas.- 3.5.1 The Case of T = 0 K.- 3.5.2 The Low-Temperature Case (T > 0 K, but T ??el).- 3.5.3 Atomic Volume, Compressibility, and Strength of Metals.- 3.5.4 Paramagnetism of a Degenerate Electron Gas.- 3.5.5 Diamagnetism of a Degenerate Electron Gas According to Landau.- 3.5.6 Oscillatory Effects in the Fermi Gas.- 3.5.7 Thermionic Emission (the Richardson Effect).- 3.6 Transport Phenomena.- 3.6.1 The Boltzmann Kinetic Equation.- 3.6.2 Electrical Conductivity.- 3.6.3 Thermal Conductivity and the Wiedemann-Franz Relation.- 3.6.4 Thermoelectric Phenomena.- 3.6.5 Galvanomagnetic Phenomena.- 3.7 High-Frequency Properties.- 3.7.1 Basic Equations.- 3.7.2 Skin Effect.- 3.7.3 Cyclotron Resonance.- 3.7.4 Electromagnetic Waves in Metals.- 3.8 Conclusions.- 4. Band Theory.- 4.1 Preliminary Observations and the One-Dimensional Model.- 4.1.1 Electron Waves in a Crystal.- 4.1.2 The Array of Rectangular Potential Barriers.- 4.1.3 Linear Atomic Array.- 4.1.4 Rigorous Theory of Electron Motion in a One-Dimensional Array.- 4.2 General Theory of the Electron Motion in a Three-Dimensional Crystal.- 4.2.1 Bloch’s Theorem.- 4.2.2 Brillouin Zones.- 4.2.3 Electron Energy Spectrum.- 4.2.4 The Properties of Constant Energy Surfaces.- 4.2.5 Density of Electron States in Energy Bands. Topological Electronic Transitions.- 4.3 Nearly-Free-Electron Approximation.- 4.3.1 Statement of the Problem.- 4.3.2 Empty-Lattice Model.- 4.3.3 Allowance for a Weak Periodic Field.- 4.4 Effect of an Electric Field on Electronic States.- 4.4.1 Acceleration and Effective Electron Mass.- 4.4.2 Zener Breakdown.- 4.4.3 Quantum Theory of the Electric Inertia Effect.- 4.5 The Metal-Semiconductor Criterion.- 4.5.1 The Metal-Nonmetal Criterion in Band Theory.- 4.5.2 The Peierls Transition.- 4.5.3 The Mott Transition.- 4.5.4 Disordered Systems.- 4.6 Computing the Electron Energy Spectrum of Crystals.- 4.6.1 Self-Consistent Field Approximation.- 4.6.2 Solving the Schrödinger Equation. Formulation of the Problem and the Cellular Method.- 4.6.3 The LCAO Method and Tight-Binding Approximation.- 4.6.4 The Orthogonalized Plane Waves (OPW) Method. Pseudopotential.- 4.6.5 The Augmented Plane Waves (APW) Method.- 4.6.6 K?P Perturbation Theory.- 4.6.7 Fermi Surfaces in Real Metals.- 4.7 Band Electrons in a Magnetic Field.- 4.7.1 The Effective Hamiltonian.- 4.7.2 Classical Paths.- 4.7.3 Quasi Classical Energy Levels. Oscillatory Effects.- 4.8 Impurity States.- 4.8.1 A Simple Model.- 4.8.2 Green’s Functions and the Density of States.- 4.8.3 Priedel Oscillations.- 4.9 The Electronic Structure of Disordered Systems.- 4.9.1 The Average Green’s Function in the Diagonal Disorder Model.- 4.9.2 Approximate Methods of Computing the Average Green’s Function in the Binary Alloy Model.- 4.9.3 Anderson Localization.- 4.10 Conclusion. The Role of Many-Particle Effects.- 5. Many-Particle Effects.- 5.1 Plasma Phenomena. Screening.- 5.1.1 A Discussion of the Model.- 5.1.2 The Equation for a Self-Consistent Plasma Potential.- 5.1.3 Static Screening.- 5.1.4 Plasmons.- 5.1.5 Phonons in the Plasma Model.- 5.1.6 Fluctuation-Dissipation Theorem.- 5.2 The Fermi-Liquid Theory.- 5.2.1 Major Postulates of the Landau Theory.- 5.2.2 Thermodynamic Properties.- 5.2.3 Kinetic Equation for Quasiparticles.- 5.3 Electron-Phonon Interaction.- 5.3.1 Formulation of the Problem.- 5.3.2 Conditions for the Applicability of the Adiabatic Approximation.- 5.3.3 Temperature Dependence of the Electrical Conductivity in Metals.- 5.3.4 Polarons.- 5.3.5 The Cooper Phenomenon.- 5.4 Superconductivity.- 5.5 Excitons.- 5.6 Transition Metals and Their Compounds.- 5.6.1 Properties of d and ƒ States.- 5.6.2 The Heisenberg Model.- 5.6.3 d Metals.- 5.6.4 Magnetism in the 4 ƒ Metals.- 5.7 Anderson’s Orthogonality Catastrophe.- 5.8 Conclusion.- Addenda (Recent Developments).- References.