Solid State Physics
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Table of contents
- Contentsv
- Prefacexii
- Chapter I. Electrons in one-dimensional periodic potentials1
- 1 The Bloch theorem for one-dimensional periodicity2
- 2 Energy levels in a periodic array of quantum wells5
- 3 Electron tunneling and energy bands8
- 4 The tight-binding approximation16
- 5 Plane waves and nearly free-electron approximation24
- 6 Some dynamical aspects of electrons in band theory29
- Further reading35
- Chapter II. Geometrical description of crystals: direct and reciprocal lattices37
- 1 Simple lattices and composite lattices38
- 2 Geometrical description of some crystal structures43
- 3 Wigner-Seitz primitive cells53
- 4 Reciprocal lattices54
- 5 Brillouin zones59
- 6 Translational symmetry and quantum mechanical aspects62
- 7 Density-of-states and critical points70
- Further reading75
- Chapter III. The Sommerfeld free-electron theory of metals77
- 1 Quantum theory of the free-electron gas77
- 2 Fermi-Dirac distribution function and chemical potential82
- 3 Electronic specific heat in metals and thermodynamic functions86
- 4 Thermionic emission from metals88
- Appendix A. Outline of statistical physics and thermodynamic relations89
- A1. Microcanonical ensemble and thermodynamic quantities89
- A2. Canonical ensemble and thermodynamic quantities91
- A3. Grand canonical ensemble and thermodynamic quantities93
- Appendix B. Fermi–Dirac and Bose–Einstein statistics for independent particles95
- Appendix C. Modified Fermi–Dirac statistics in a model of correlation effects98
- Further reading100
- Chapter IV. The one-electron approximation and beyond102
- 1 Introductory remarks on the many-electron problem103
- 2 The Hartree equations104
- 3 Identical particles and determinantal wavefunctions106
- 4 Matrix elements between determinantal states107
- 5 The Hartree-Fock equations110
- 6 Overview of approaches beyond the one-electron approximation121
- 7 Electronic properties and phase diagram of the homogeneous electron gas122
- 8 The density functional theory and the Kohn-Sham equations130
- Appendix A. Bielectronic integrals among spin-orbitals137
- Appendix B. Outline of second quantization formalism for identical fermions138
- Appendix C. An integral on the Fermi sphere141
- Further reading142
- Chapter V. Band theory of crystals143
- 1 Basic assumptions of the band theory143
- 2 The tight-binding method (LCAO method)145
- 3 The orthogonalized plane wave (OPW) method154
- 4 The pseudopotential method163
- 5 The cellular method169
- 6 The augmented plane wave (APW) method171
- 7 The Green's function method (KKR method)177
- 8 Other methods and developments in electronic structure calculations184
- Further reading196
- Chapter VI. Electronic properties of selected crystals199
- 1 Band structure and cohesive energy of rare-gas solids200
- 2 Electronic properties of ionic crystals207
- 3 Covalent crystals with diamond structure218
- 4 Band structures and Fermi surfaces of some metals222
- Further reading228
- Chapter VII. Excitons, plasmons and dielectric screening in crystals230
- 1 Exciton states in crystals231
- 2 Plasmon excitations in crystals239
- 3 General considerations on the longitudinal dielectric function240
- 4 Static dielectric screening in metals with the Thomas-Fermi model242
- 5 Static dielectric screening in metals with the Lindhard model245
- 6 Dynamic dielectric screening in metals and plasmon modes250
- 7 Quantum expression of the longitudinal dielectric function in materials254
- 8 Quantum expression of the longitudinal dielectric function in crystals259
- 9 Longitudinal dielectric function and energy-loss of a fast charged particle262
- Appendix A. Lindhard dielectric function for the free-electron gas263
- Further reading266
- Chapter VIII. Interacting electronic–nuclear systems and the adiabatic principle268
- 1 Electronic-nuclear systems and adiabatic potential-energy surfaces269
- 2 Non-degenerate adiabatic surface and nuclear dynamics272
- 3 Degenerate adiabatic surfaces and Jahn–Teller systems278
- 4 The Hellmann–Feynman theorem and electronic–nuclear systems294
- 5 Parametric Hamiltonians and Berry phase297
- 6 Macroscopic electric polarization in crystals and Berry phase301
- Further reading305
- Chapter IX. Lattice dynamics of crystals307
- 1 Dynamics of monatomic one-dimensional lattices308
- 2 Dynamics of diatomic one-dimensional lattices312
- 3 Dynamics of general three-dimensional crystals315
- 4 Quantum theory of the harmonic crystal323
- 5 Lattice heat capacity. Einstein and Debye models325
- 6 Considerations on anharmonic effects and melting of solids327
- 7 Optical phonons and polaritons in polar crystals329
- Appendix A. Quantum theory of the Linear harmonic oscillator344
- Further reading348
- Chapter X. Scattering of particles by crystals349
- 1 General considerations349
- 2 Elastic scattering of X-rays from crystals352
- 3 Inelastic scattering of particles and phonon spectra of crystals363
- 4 Compton scattering and electron momentum density368
- 5 Diffusion of particles by a single elastically-bound scatterer373
- 6 Diffusion of particles by a crystal and effects of lattice vibrations380
- 7 Mössbauer effect384
- Further reading387
- Chapter XI. Optical and transport properties in metals389
- 1 Macroscopic theory of optical constants in homogeneous materials390
- 2 The Drude theory of the optical properties of free carriers395
- 3 Transport properties and Boltzmann equation403
- 4 Static and dynamic conductivity in metals406
- 5 Boltzmann treatment and quantum treatment of intraband transitions413
- 6 The Boltzmann equation in electric fields and temperature gradients414
- Further reading424
- Chapter XII. Optical properties of semiconductors and insulators425
- 1 Quantum expression of the transverse dielectric function in materials426
- 2 Quantum theory of band-to-band optical transitions and critical points433
- 3 Indirect phonon-assisted transitions438
- 4 Two-photon absorption443
- 5 Exciton effects on the optical properties446
- 6 Fano resonances and absorption lineshapes452
- 7 Optical properties of vibronic systems458
- Appendix A. Transitions rates at first and higher orders of perturbation theory469
- Further reading471
- Chapter XIII. Transport in intrinsic and homogeneously doped semiconductors473
- 1 Fermi level and carrier density in intrinsic semiconductors473
- 2 Impurity levels in semiconductors478
- 3 Fermi level and carrier density in doped semiconductors485
- 4 Thermionic emission in semiconductors490
- 5 Non-equilibrium carrier distributions491
- 6 Solutions of typical transport equations in uniformly doped semiconductors498
- Further reading504
- Chapter XIV. Transport in inhomogeneous semiconductors506
- 1 Properties of the pn junction at equilibrium506
- 2 Current–voltage characteristics of the pn junction512
- 3 The bipolar junction transistor517
- 4 The junction field-effect transistor (JFET)520
- 5 Semiconductor heterojunctions524
- 6 Metal–semiconductor contacts and MESFET transistor527
- 7 The metal–oxide–semiconductor structure and MOSFET transistor533
- Further reading541
- Chapter XV. Electron gas in magnetic fields543
- 1 Magnetization and magnetic susceptibiity544
- 2 Energy levels and density-of-states of a free-electron gas in magnetic fields546
- 3 Orbital magnetic susceptibility and de Haas–van Alphen effect554
- 4 Spin paramagnetism of a free-electron gas562
- 5 Magnetoresistivity and classical Hall effect564
- 6 The quantum Hall effect569
- Appendix A. Free energy of an electron gas in a uniform magnetic field574
- Appendix B. Generalized orbital magnetic susceptibility of the free-electron gas579
- Further reading585
- Chapter XVI. Magnetic properties of localized systems and Kondo impurities586
- 1 Quantum mechanical treatment of magnetic susceptibility587
- 2 Magnetic susceptibility of closed-shell systems589
- 3 Permanent magnetic dipoles in atoms or ions with partially filled shells591
- 4 Paramagnetism of localized magnetic moments593
- 5 Localized magnetic states in normal metals598
- 6 Dilute magnetic alloys and the resistance minimum phenomenon602
- 7 Magnetic impurity in normal metals at very low temperatures612
- Further reading618
- Chapter XVII. Magnetic ordering in crystals619
- 1 Ferromagnetism and the Weiss molecular field620
- 2 Microscopic origin of the coupling between localized magnetic moments627
- 3 Antiferromagnetism in the mean field approximation635
- 4 Spin waves and magnons in ferromagnetic crystals638
- 5 The Ising model with the transfer matrix method643
- 6 The Ising model with the renormalization group theory647
- 7 The Stoner–Hubbard itinerant electron model for magnetism659
- Further reading662
- Chapter XVIII. Superconductivity663
- 1 Some phenomenolgical aspects of superconductors664
- 2 The Cooper pair idea672
- 3 Ground state for a superconductor in the BCS theory at zero temperature678
- 4 Excited states of superconductors at zero temperature686
- 5 Treatment of superconductors at finite temperature and heat capacity693
- 6 Diamagnetism of superconductors and Meissner effect698
- 7 Macroscopic quantum phenomena704
- 8 Cooper pair tunneling between superconductors and Josephson effects711
- Appendix A. The phonon–induced electron-electron interaction717
- Further reading720
- Subject index722
Although there are many books published in solid state physics, there is a wide gap between the active field of research and the concepts
traditionally taught in solid state courses. This book fills that gap. The style is tutorial, simple, and completely self-contained.
Solid State Physicsexplains to readers the newest advances in the area of condensed matter physics with rigorous, but lucid mathematics. Examples are an integral part of the text, and they are carefully designed to apply the fundamental principles illustrated in the text to currently active topics of research.
Key Features
* Bridges the gap between fundamental principles and active fields of reserch, including explanations of all the latest advances
* Provides an in-depth treatment of current research topics
* Examples are integral to the text and apply fundamental principles to current topics of research
* Both authors have many years of experience of teaching at a variety of levels--undergraduate, post-graduate, tutorial workshops and seminars
traditionally taught in solid state courses. This book fills that gap. The style is tutorial, simple, and completely self-contained.
Solid State Physicsexplains to readers the newest advances in the area of condensed matter physics with rigorous, but lucid mathematics. Examples are an integral part of the text, and they are carefully designed to apply the fundamental principles illustrated in the text to currently active topics of research.
Key Features
* Bridges the gap between fundamental principles and active fields of reserch, including explanations of all the latest advances
* Provides an in-depth treatment of current research topics
* Examples are integral to the text and apply fundamental principles to current topics of research
* Both authors have many years of experience of teaching at a variety of levels--undergraduate, post-graduate, tutorial workshops and seminars