Preface |

Electrons in one-dimensional periodic potentials / Chapter I： |

The Bloch theorem for one-dimensional periodicity / 1： |

Energy levels in a periodic array of quantum wells / 2： |

Electron tunneling and energy bands / 3： |

Transmission and reflection of electrons through an arbitrary potential / 3.1： |

Electron tunneling through a periodic potential / 3.2： |

The tight-binding approximation / 4： |

Expansion in localized orbitals / 4.1： |

Tridiagonal matrices and continued fractions / 4.2： |

Plane waves and nearly free-electron approximation / 5： |

Expansion in plane waves / 5.1： |

The Mathieu potential and the continued fraction solution / 5.2： |

Some dynamical aspects of electrons in band theory / 6： |

Further reading |

Geometrical description of crystals: direct and reciprocal lattices / Chapter II： |

Simple lattices and composite lattices |

Periodicity and Bravais lattices / 1.1： |

Simple and composite crystal structures / 1.2： |

Geometrical description of some crystal structures |

Wigner-Seitz primitive cells |

Reciprocal lattices |

Definitions and basic properties |

Planes and directions in Bravais lattices |

Brillouin zones |

Translational symmetry and quantum mechanical aspects |

Translational symmetry and Bloch wavefunctions / 6.1： |

The parametric k [times] p Hamiltonian / 6.2： |

Cyclic boundary conditions / 6.3： |

Special k points for averaging over the Brillouin zone / 6.4： |

Density-of-states and critical points / 7： |

The Sommerfeld free-electron theory of metals / Chapter III： |

Quantum theory of the free-electron gas |

Fermi-Dirac distribution function and chemical potential |

Electronic specific heat in metals and thermodynamic functions |

Thermionic emission from metals |

Outline of statistical physics and thermodynamic relations / Appendix A.： |

Microcanonical ensemble and thermodynamic quantities / A1.： |

Canonical ensemble and thermodynamic quantities / A2.： |

Grand canonical ensemble and thermodynamic quantities / A3.： |

Fermi-Dirac and Bose-Einstein statistics for independent particles / Appendix B.： |

Modified Fermi-Dirac statistics in a model of correlation effects / Appendix C.： |

The one-electron approximation and beyond / Chapter IV： |

Introductory remarks on the many-electron problem |

The Hartree equations |

Identical particles and determinantal wavefunctions |

Matrix elements between determinantal states |

The Hartree-Fock equations |

Variational approach and Hartree-Fock equations |

Ground-state energy, ionization energies and transition energies |

Hartree-Fock equations and transition energies in closed-shell systems / 5.3： |

Hartree-Fock-Slater and Hartree-Fock-Roothaan approximations / 5.4： |

Overview of approaches beyond the one-electron approximation |

Electronic properties and phase diagram of the homogeneous electron gas |

The density functional theory and the Kohn-Sham equations / 8： |

Bielectronic integrals among spin-orbitals |

Outline of second quantization formalism for identical fermions |

An integral on the Fermi sphere |

Band theory of crystals / Chapter V： |

Basic assumptions of the band theory |

The tight-binding method (LCAO method) |

Description of the method for simple lattices / 2.1： |

Description of the tight-binding method for composite lattices / 2.2： |

Illustrative applications of the tight-binding scheme / 2.3： |

The orthogonalized plane wave (OPW) method |

The pseudopotential method |

The cellular method |

The augmented plane wave (APW) method |

Description of the method |

Expression and evaluation of the matrix elements of the APW method |

The Green's function method (KKR method) |

Scattering integral equation for a generic potential / 7.1： |

Scattering integral equation for a periodic muffin-tin potential / 7.2： |

Expression and evaluation of the structure coefficients / 7.3： |

Other methods and developments in electronic structure calculations |

The linearized cellular methods / 8.1： |

The Lanczos or recursion method / 8.2： |

Modified Lanczos method for excited states / 8.3： |

Renormalization method for electronic systems / 8.4： |

Electronic properties of selected crystals / Chapter VI： |

Band structure and cohesive energy of rare-gas solids |

General features of band structure of rare-gas solids |

Cohesive energy of rare-gas solids |

Electronic properties of ionic crystals |

Introductory remarks and Madelung constant |

Considerations on bands and bonds in ionic crystals |

Covalent crystals with diamond structure |

Band structures and Fermi surfaces of some metals |

Excitons, plasmons and dielectric screening in crystals / Chapter VII： |

Exciton states in crystals |

Plasmon excitations in crystals |

General considerations on the longitudinal dielectric function |

Static dielectric screening in metals with the Thomas-Fermi model |

Static dielectric screening in metals with the Lindhard model |

Dynamic dielectric screening in metals and plasmon modes |

Quantum expression of the longitudinal dielectric function in materials |

Quantum expression of the longitudinal dielectric function in crystals |

Longitudinal dielectric function and energy-loss of a fast charged particle / 9： |

Lindhard dielectric function for the free-electron gas |

Interacting electronic-nuclear systems and the adiabatic principle / Chapter VIII： |

Electronic-nuclear systems and adiabatic potential-energy surfaces |

Non-degenerate adiabatic surface and nuclear dynamics |

Non-degenerate adiabatic surface and classical nuclear dynamics |

Non-degenerate adiabatic surface and quantum nuclear dynamics |

Degenerate adiabatic surfaces and Jahn-Teller systems |

Degenerate adiabatic surfaces and nuclear dynamics |

The Jahn-Teller effect for doubly degenerate electronic states |

The Jahn-Teller effect for triply degenerate electronic states / 3.3： |

The Hellmann-Feynman theorem and electronic-nuclear systems |

General considerations on the Hellmann-Feynman theorem |

Charge density and atomic forces |

Parametric Hamiltonians and Berry phase |

Macroscopic electric polarization in crystals and Berry phase |

Lattice dynamics of crystals / Chapter IX： |

Dynamics of monatomic one-dimensional lattices |

Dynamics of diatomic one-dimensional lattices |

Dynamics of general three-dimensional crystals |

Quantum theory of the harmonic crystal |

Lattice heat capacity. Einstein and Debye models |

Considerations on anharmonic effects and melting of solids |

Optical phonons and polaritons in polar crystals |

General considerations |

Lattice vibrations in polar crystals and polaritons |

Local field effects on polaritons |

Quantum theory of the linear harmonic oscillator |

Scattering of particles by crystals / Chapter X： |

Elastic scattering of X-rays from crystals |

Elastic scattering of X-rays and Bragg diffraction condition |

Elastic scattering of X-rays and intensity of diffracted beams |

Inelastic scattering of particles and phonon spectra of crystals |

Compton scattering and electron momentum density |

Diffusion of particles by a single elastically-bound scatterer |

Dynamical structure factor of a single scattering center |

Dynamical structure factor of a three-dimensional harmonic oscillator |

Diffusion of particles by a crystal and effects of lattice vibrations |

Mossbauer effect |

Optical and transport properties in metals / Chapter XI： |

Macroscopic theory of optical constants in homogeneous materials |

The Drude theory of the optical properties of free carriers |

Transport properties and Boltzmann equation |

Static and dynamic conductivity in metals |

Static conductivity with the Boltzmann equation |

Frequency and wavevector dependence of the conductivity |

Anomalous skin effect / 4.3： |

Boltzmann treatment and quantum treatment of intraband transitions |

The Boltzmann equation in electric fields and temperature gradients |

The transport equations in general form |

Thermoelectric phenomena |

Optical properties of semiconductors and insulators / Chapter XII： |

Quantum expression of the transverse dielectric function in materials |

Optical constants of homogeneous media in the linear response theory |

Optical constants and Green's function of the electronic system |

Quantum theory of band-to-band optical transitions and critical points |

Indirect phonon-assisted transitions |

Two-photon absorption |

Exciton effects on the optical properties |

Fano resonances and absorption lineshapes |

Optical properties of vibronic systems |

Optical properties of the Frank-Condon vibronic model |

Optical properties of typical Jahn-Teller systems |

Transitions rates at first and higher orders of perturbation theory |

Transport in intrinsic and homogeneously doped semiconductors / Chapter XIII： |

Fermi level and carrier density in intrinsic semiconductors |

Impurity levels in semiconductors |

Fermi level and carrier density in doped semiconductors |

Thermionic emission in semiconductors |

Non-equilibrium carrier distributions |

Drift and diffusion currents |

Generation and recombination of electron-hole pairs in semiconductors |

Solutions of typical transport equations in uniformly doped semiconductors |

Transport in inhomogeneous semiconductors / Chapter XIV： |

Properties of the pn junction at equilibrium |

Current-voltage characteristics of the pn junction |

The bipolar junction transistor |

The junction field-effect transistor (JFET) |

Semiconductor heterojunctions |

Metal-semiconductor contacts and MESFET transistor |

The metal-oxide-semiconductor structure and MOSFET transistor |

Electron gas in magnetic fields / Chapter XV： |

Magnetization and magnetic susceptibility |

Energy levels and density-of-states of a free-electron gas in magnetic fields |

Energy levels of the two-dimensional electron gas in magnetic fields |

Energy levels of the three-dimensional electron gas in magnetic fields |

Orbital magnetic susceptibility and de Haas-van Alphen effect |

Orbital magnetic susceptibility of a two-dimensional electron gas |

Orbital magnetic susceptibility of a three-dimensional electron gas |

Spin paramagnetism of a free-electron gas |

Magnetoresistivity and classical Hall effect |

The quantum Hall effect |

Free energy of an electron gas in a uniform magnetic field |

Generalized orbital magnetic susceptibility of the free-electron gas |

Magnetic properties of localized systems and Kondo impurities / Chapter XVI： |

Quantum mechanical treatment of magnetic susceptibility |

Magnetic susceptibility of closed-shell systems |

Permanent magnetic dipoles in atoms or ions with partially filled shells |

Paramagnetism of localized magnetic moments |

Localized magnetic states in normal metals |

Dilute magnetic alloys and the resistance minimum phenomenon |

Some phenomenological aspects |

The resistance minimum phenomenon |

Microscopic origin of the Kondo interaction: a molecular model |

Magnetic impurity in normal metals at very low temperatures |

Magnetic ordering in crystals / Chapter XVII： |

Ferromagnetism and the Weiss molecular field |

Microscopic origin of the coupling between localized magnetic moments |

Antiferromagnetism in the mean field approximation |

Spin waves and magnons in ferromagnetic crystals |

The Ising model with the transfer matrix method |

The Ising model with the renormalization group theory |

The Stoner-Hubbard itinerant electron model for magnetism |

Superconductivity / Chapter XVIII： |

Some phenomenological aspects of superconductors |

The Cooper pair idea |

Ground state for a superconductor in the BCS theory at zero temperature |

Variational determination of the ground-state wavefunction |

Ground-state energy and isotopic effect |

Momentum distribution and coherence length |

Excited states of superconductors at zero temperature |

The Bogoliubov canonical transformation |

Persistent currents in superconductors |

Electron tunneling into superconductors |

Treatment of superconductors at finite temperature and heat capacity |

Diamagnetism of superconductors and Meissner effect |

The phenomenological London model |

Pippard electrodynamics and effective magnetic penetration depth |

Macroscopic quantum phenomena |

Order parameter in superconductors and Ginzburg-Landau theory |

Magnetic flux quantization |

Type-I and type-II superconductors |

Cooper pair tunneling between superconductors and Josephson effects |

The phonon-induced electron-electron interaction |

Subject index |