Introduction to Solid-State Theory

ISBN-13: 9783540604433 / Angielski / Miękka / 1995 / 491 str.

Otfried Madelung;B.C. Taylor

Opis

Introduction to Solid-State Theory is a textbook for graduate students of physics and materials science. It also provides the theoretical background needed by physicists doing research in pure solid-state physics and its applications to electrical engineering. The fundamentals of solid-state theory are based on a description by delocalized and localized states and - within the concept of delocalized states - by elementary excitations. The development of solid-state theory within the last ten years has shown that by a systematic introduction of these concepts, large parts of the theory can be described in a unified way. This form of description gives a "pictorial" formulation of many elementary processes in solids, which facilitates their understanding.

Recenzje

FROM THE REVIEWS:

ZEITSCHRIFT FUR PHYSIKALISCHE CHEMIE
"...the textbook is an excellent introduction into most fields of modern solid state theory and may be recommended to...graduate students in physics and material sciences as well as researchers in the field of solid state physics."

PHYSICALIA
"...the book is remarkably well articulated and its organization is crystal-clear...Because this book requires a good-knowledge of quantum mechanics and also some prior knowledge of the most important solid-state phenomena, we shall recommend it to advanced graduate students or researchers, having already been introduced to the solid-state physics. They shall find in it a systematic introduction of the concepts of solid-state theory, presented in a unified way, that is illuminating from many points of view."

Spis treści

1. Fundamentals.- 1.1 Introduction.- 1.2 The Basic Hamiltonian.- 1.3 The Hartree-Fock Approximation.- 2. The One-Electron Approximation.- 2.1 The Electron Gas Without Interaction.- 2.1.1 Introduction.- 2.1.2 The Energy States.- 2.1.3 Excited States.- 2.1.4 The Fermi Distribution.- 2.1.5 Free Electrons in an Electric Field.- 2.1.6 Free Electrons in a Magnetic Field.- 2.1.7 Dia- and Paramagnetism of Free Electrons, the de Haasvan Alphen Effect.- 2.2 Electrons in a Periodic Potential.- 2.2.1 Introduction.- 2.2.2 The Symmetries of the Crystal Lattice.- 2.2.3 The Schrödinger Equation for Electrons in a Periodic Potential.- 2.2.4 The Reciprocal Lattice, Bragg Reflections.- 2.2.5 Consequences of Translational Invariance.- 2.2.6 Nearly Free Electron Approximation.- 2.2.7 Wannier Functions, LCAO Approximation.- 2.2.8 General Properties of the Function En(k).- 2.2.9 Dynamics of Crystal Electrons.- 2.2.10 The Density of States in the Band Model.- 2.2.11 The Band Structure of Metals, Fermi Surfaces.- 2.2.12 The Band Structure of Semiconductors and Insulators.- 2.2.13 Consequences of the Invariance of the Hamiltonian to Symmetry Operations of the Space Group.- 2.2.14 Irreducible Representations of Space Groups.- 2.2.15 Spin, Time Reversal.- 2.2.16 Pseudopotentials.- 3. Elementary Excitations.- 3.1 The Interacting Electron Gas: Quasi-Electrons and Plasmons.- 3.1.1 Introduction.- 3.1.2 The Coulomb Interaction.- 3.1.3 The Hartree-Fock Approximation for the Electron Gas.- 3.1.4 Screening, Plasmons.- 3.1.5 Quasi-Electrons.- 3.1.6 The Dielectric Constant of the Electron Gas.- 3.2 Electron-Hole Interaction in Semiconductors and Insulators: Excitons.- 3.2.1 Introduction.- 3.2.2 The Ground State of the Insulator in Bloch and Wannier Representation.- 3.2.3 Excited States, the Exciton Representation.- 3.2.4 Wannier Excitons.- 3.2.5 Frenkel Excitons.- 3.2.6 Excitons as Elementary Excitations.- 3.3 Ion-Ion Interaction: Phonons.- 3.3.1 Introduction.- 3.3.2 The Classical Equations of Motion.- 3.3.3 Normal Coordinates, Phonons.- 3.3.4 The Energy Content of the Lattice Vibrations, Specific Heat.- 3.3.5 Calculation of Phonon Dispersion Relations.- 3.3.6 The Density of States.- 3.3.7 The Long Wavelength Limit: Acoustic Branch.- 3.3.8 The Long Wavelength Limit: Optical Branch.- 3.4 Spin-Spin Interaction: Magnons.- 3.4.1 Introduction.- 3.4.2 Spin Waves in Ferromagnets: Magnons.- 3.4.3 Spin Waves in Lattices with a Basis, Ferri-, and Antiferromagnetism.- 3.4.4 Ferromagnetism Near the Curie Temperature.- 3.4.5 Ordered Magnetism of Valence and Conduction Electrons, the Collective Electron Model.- 4. Electron-Phonon Interaction: Transport Phenomena.- 4.1 The Interaction Processes.- 4.1.1 Introduction.- 4.1.2 Interaction of Electrons with Acoustic Phonons.- 4.1.3 Electron-Phonon Interaction in Polar Solids, Polarons.- 4.2 The Boltzmann Equation.- 4.2.1 Introduction.- 4.2 Boltzmann Equations for the Electron and Phonon Systems.- 4.2.3 The Relaxation Time Approximation.- 4.2.4 The Variational Method.- 4.3 Formal Transport Theory.- 4.3.1 The Transport Equations.- 4.3.2 Transport Coefficients Without a Magnetic Field.- 4.3.3 Transport Coefficients with a Magnetic Field.- 4.4 Transport in Metals and Semiconductors.- 4.4.1 The Electrical Conductivity.- 4.4.2 Transport Coefficients in the Relaxation Time Approximation.- 4.4.3 Limits of Validity and Possible Extensions of the Approximations Used.- 5. Electron-Electron Interaction by Exchange of Virtual Phonons: Superconductivity.- 5.1 Introduction.- 5.2 Cooper Pairs.- 5.3 The Ground State of the Superconducting Electron Gas.- 5.4 Excited States.- 5.5 Comparison with Experiment.- 5.6 Thc Meissner-Ochsenfeld Effect.- 5.7 Further Theoretical Concepts.- 6. Interaction with Photons: Optics.- 6.1 Fundamentals.- 6.1.1 Introduction.- 6.1.2 Photons.- 6.1.3 Polaritons.- 6.1.4 The Complex Dielectric Constant.- 6.2 Electron-Photon Interaction.- 6.2.1 Introduction.- 6.2.2 Direct Transitions.- 6.2.3 Indirect Transitions.- 6.2.4 Two-Photon Absorption.- 6.2.5 Exciton Absorption.- 6.2.6 Comparison with Experimental Absorption and Reflection Spectra.- 6.2.7 Absorption by Free Charge Carriers.- 6.2.8 Absorption and Reflection in a Magnetic Field.- 6.2.9 Magneto-Optics of Free Charge Carriers.- 6.3 Phonon-Photon Interaction.- 6.3.1 Introduction.- 6.3.2 One-Phonon Absorption.- 6.3.3 Multi-Phonon Absorption.- 6.3.4 Raman and Brillouin Scattering.- 7. Phonon-Phonon Interaction: Thermal Properties.- 7.1 Introduction.- 7.2 Frequency Shift and Lifetime of Phonons.- 7.3 The Anharmonic Contributions to the Free Energy, Thermal Expansion.- 7.4 The Thermal Conductivity of the Lattice.- 8. Local Description of Solid-State Properties.- 8.1 Localized and Extended States.- 8.2 The Chemical Bond.- 8.2.1 Introduction.- 8.2.2 The Localized Single Bond.- 8.2.3 Localized and Delocalized Bonds.- 8.2.4 Solids with Localized Bonds: Insulators and Semiconductors.- 8.2.5 The Dielectric Theory of the Covalent Bond.- 8.2.6 Solids with Delocalized Bonds: Metals.- 8.3 Local Versus Nonlocal Description in Unperturbed Lattices.- 8.3.1 Introduction.- 8.3.2 Correlations, the Hubbard Model.- 8.3.3 Metal-Insulator Transitions.- 8.3.4 Limits of the Boltzmann Equation, the Kubo and Kubo-Greenwood Formulae.- 8.3.5 The Small Polaron.- 8.3.6 Hopping Conductivity in Polar Solids.- 9. Localized States.- 9.1 Point Imperfections.- 9.1.1 Introduction.- 9.1.2 Description Within the Framework of the Band Model.- 9.1.3 Crystal Field Theory.- 9.1.4 Localized Lattice Vibrations.- 9.1.5 Defect Statistics, Reaction Kinetics.- 9.1.6 Disorder Equilibria.- 9.1.7 Diffusion and Ionic Conduction.- 9.1.8 Recombination Processes at Imperfections.- 9.1.9 Optical Transitions at Imperfections, Configuration Coordinates.- 9.1.10 Electron-Phonon Interaction at Imperfections.- 9.1.11 Bound Excitons.- 9.1.12 Imperfections as Scattering Centres, the Kondo Effect.- 9.2 Localized States and Elementary Excitations at Surfaces.- 9.2.1 Introduction.- 9.2.2 Electronic Surface States.- 9.2.3 Surface-Phonons, -Polaritons, and -Plasmons.- 10. Disorder.- 10.1 Localized States in Disordered Lattices.- 10.1.1 Introduction.- 10.1.2 Localized States.- 10.1.3 Density of States.- 10.2 Transport in Disordered Lattices.- 10.2.1 Transport in Extended States.- 10.2 The Hopping Probability.- 10.2.3 Fixed Range and Variable Range Hopping.- 10.2.4 Conductivity in Impurity Bands and in Amorphous Semiconductors.- Appendix: The Occupation Number Representation.- Problems to Chapters 1–9.

Blurb

Introduction to Solid-State Theory is a textbook for graduate students of physics and materials science. It also provides the theoretical background needed by physicists doing research in pure solid-state physics and its applications to electrical engineering. The fundamentals of solid-state theory are based on a description by delocalized and localized states and - within the concept of delocalized states - by elementary excitations. The development of solid-state theory within the last ten years has shown that by a systematic introduction of these concepts, large parts of the theory can be described in a unified way. At the same time, this form of description gives a "pictorial" formulation of many elementary processes in solids, which facilitates their understanding.