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 |