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| Preface | |
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| Electrons in one-dimensional periodic potentials | |
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| The Bloch theorem for one-dimensional periodicity | |
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| Energy levels in a periodic array of quantum wells | |
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| Electron tunneling and energy bands | |
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| Transmission and reflection of electrons through an arbitrary potential | |
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| Electron tunneling through a periodic potential | |
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| The tight-binding approximation | |
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| Expansion in localized orbitals | |
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| Tridiagonal matrices and continued fractions | |
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| Plane waves and nearly free-electron approximation | |
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| Expansion in plane waves | |
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| The Mathieu potential and the continued fraction solution | |
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| Some dynamical aspects of electrons in band theory | |
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| Further reading | |
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| Geometrical description of crystals: direct and reciprocal lattices | |
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| Simple lattices and composite lattices | |
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| Periodicity and Bravais lattices | |
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| Simple and composite crystal structures | |
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| Geometrical description of some crystal structures | |
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| Wigner-Seitz primitive cells | |
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| Reciprocal lattices | |
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| Definitions and basic properties | |
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| Planes and directions in Bravais lattices | |
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| Brillouin zones | |
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| Translational symmetry and quantum mechanical aspects | |
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| Translational symmetry and Bloch wavefunctions | |
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| The parametric k [times] p Hamiltonian | |
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| Cyclic boundary conditions | |
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| Special k points for averaging over the Brillouin zone | |
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| Density-of-states and critical points | |
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| Further reading | |
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| The Sommerfeld free-electron theory of metals | |
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| Quantum theory of the free-electron gas | |
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| Fermi-Dirac distribution function and chemical potential | |
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| Electronic specific heat in metals and thermodynamic functions | |
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| Thermionic emission from metals | |
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| Outline of statistical physics and thermodynamic relations | |
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| Microcanonical ensemble and thermodynamic quantities | |
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| Canonical ensemble and thermodynamic quantities | |
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| Grand canonical ensemble and thermodynamic quantities | |
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| Fermi-Dirac and Bose-Einstein statistics for independent particles | |
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| Modified Fermi-Dirac statistics in a model of correlation effects | |
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| Further reading | |
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| The one-electron approximation and beyond | |
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| Introductory remarks on the many-electron problem | |
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| The Hartree equations | |
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| Identical particles and determinantal wavefunctions | |
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| Matrix elements between determinantal states | |
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| The Hartree-Fock equations | |
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| Variational approach and Hartree-Fock equations | |
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| Ground-state energy, ionization energies and transition energies | |
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| Hartree-Fock equations and transition energies in closed-shell systems | |
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| Hartree-Fock-Slater and Hartree-Fock-Roothaan approximations | |
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| Overview of approaches beyond the one-electron approximation | |
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| Electronic properties and phase diagram of the homogeneous electron gas | |
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| The density functional theory and the Kohn-Sham equations | |
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| Bielectronic integrals among spin-orbitals | |
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| Outline of second quantization formalism for identical fermions | |
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| An integral on the Fermi sphere | |
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| Further reading | |
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| Band theory of crystals | |
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| Basic assumptions of the band theory | |
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| The tight-binding method (LCAO method) | |
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| Description of the method for simple lattices | |
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| Description of the tight-binding method for composite lattices | |
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| Illustrative applications of the tight-binding scheme | |
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| The orthogonalized plane wave (OPW) method | |
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| The pseudopotential method | |
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| The cellular method | |
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| The augmented plane wave (APW) method | |
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| Description of the method | |
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| Expression and evaluation of the matrix elements of the APW method | |
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| The Green's function method (KKR method) | |
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| Scattering integral equation for a generic potential | |
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| Scattering integral equation for a periodic muffin-tin potential | |
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| Expression and evaluation of the structure coefficients | |
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| Other methods and developments in electronic structure calculations | |
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| The linearized cellular methods | |
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| The Lanczos or recursion method | |
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| Modified Lanczos method for excited states | |
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| Renormalization method for electronic systems | |
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| Further reading | |
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| Electronic properties of selected crystals | |
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| Band structure and cohesive energy of rare-gas solids | |
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| General features of band structure of rare-gas solids | |
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| Cohesive energy of rare-gas solids | |
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| Electronic properties of ionic crystals | |
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| Introductory remarks and Madelung constant | |
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| Considerations on bands and bonds in ionic crystals | |
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| Covalent crystals with diamond structure | |
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| Band structures and Fermi surfaces of some metals | |
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| Further reading | |
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| Excitons, plasmons and dielectric screening in crystals | |
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| Exciton states in crystals | |
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| Plasmon excitations in crystals | |
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| General considerations on the longitudinal dielectric function | |
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| Static dielectric screening in metals with the Thomas-Fermi model | |
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| Static dielectric screening in metals with the Lindhard model | |
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| Dynamic dielectric screening in metals and plasmon modes | |
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| Quantum expression of the longitudinal dielectric function in materials | |
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| Quantum expression of the longitudinal dielectric function in crystals | |
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| Longitudinal dielectric function and energy-loss of a fast charged particle | |
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| Lindhard dielectric function for the free-electron gas | |
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| Further reading | |
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| Interacting electronic-nuclear systems and the adiabatic principle | |
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| Electronic-nuclear systems and adiabatic potential-energy surfaces | |
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| Non-degenerate adiabatic surface and nuclear dynamics | |
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| Non-degenerate adiabatic surface and classical nuclear dynamics | |
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| Non-degenerate adiabatic surface and quantum nuclear dynamics | |
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| Degenerate adiabatic surfaces and Jahn-Teller systems | |
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| Degenerate adiabatic surfaces and nuclear dynamics | |
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| The Jahn-Teller effect for doubly degenerate electronic states | |
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| The Jahn-Teller effect for triply degenerate electronic states | |
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| The Hellmann-Feynman theorem and electronic-nuclear systems | |
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| General considerations on the Hellmann-Feynman theorem | |
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| Charge density and atomic forces | |
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| Parametric Hamiltonians and Berry phase | |
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| Macroscopic electric polarization in crystals and Berry phase | |
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| Further reading | |
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| Lattice dynamics of crystals | |
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| Dynamics of monatomic one-dimensional lattices | |
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| Dynamics of diatomic one-dimensional lattices | |
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| Dynamics of general three-dimensional crystals | |
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| Quantum theory of the harmonic crystal | |
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| Lattice heat capacity. Einstein and Debye models | |
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| Considerations on anharmonic effects and melting of solids | |
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| Optical phonons and polaritons in polar crystals | |
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| General considerations | |
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| Lattice vibrations in polar crystals and polaritons | |
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| Local field effects on polaritons | |
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| Quantum theory of the linear harmonic oscillator | |
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| Further reading | |
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| Scattering of particles by crystals | |
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| General considerations | |
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| Elastic scattering of X-rays from crystals | |
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| Elastic scattering of X-rays and Bragg diffraction condition | |
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| Elastic scattering of X-rays and intensity of diffracted beams | |
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| Inelastic scattering of particles and phonon spectra of crystals | |
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| Compton scattering and electron momentum density | |
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| Diffusion of particles by a single elastically-bound scatterer | |
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| Dynamical structure factor of a single scattering center | |
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| Dynamical structure factor of a three-dimensional harmonic oscillator | |
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| Diffusion of particles by a crystal and effects of lattice vibrations | |
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| Mossbauer effect | |
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| Further reading | |
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| Optical and transport properties in metals | |
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| Macroscopic theory of optical constants in homogeneous materials | |
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| The Drude theory of the optical properties of free carriers | |
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| Transport properties and Boltzmann equation | |
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| Static and dynamic conductivity in metals | |
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| Static conductivity with the Boltzmann equation | |
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| Frequency and wavevector dependence of the conductivity | |
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| Anomalous skin effect | |
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| Boltzmann treatment and quantum treatment of intraband transitions | |
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| The Boltzmann equation in electric fields and temperature gradients | |
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| The transport equations in general form | |
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| Thermoelectric phenomena | |
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| Further reading | |
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| Optical properties of semiconductors and insulators | |
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| Quantum expression of the transverse dielectric function in materials | |
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| Optical constants of homogeneous media in the linear response theory | |
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| Optical constants and Green's function of the electronic system | |
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| Quantum theory of band-to-band optical transitions and critical points | |
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| Indirect phonon-assisted transitions | |
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| Two-photon absorption | |
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| Exciton effects on the optical properties | |
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| Fano resonances and absorption lineshapes | |
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| Optical properties of vibronic systems | |
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| Optical properties of the Frank-Condon vibronic model | |
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| Optical properties of typical Jahn-Teller systems | |
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| Transitions rates at first and higher orders of perturbation theory | |
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| Further reading | |
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| Transport in intrinsic and homogeneously doped semiconductors | |
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| Fermi level and carrier density in intrinsic semiconductors | |
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| Impurity levels in semiconductors | |
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| Fermi level and carrier density in doped semiconductors | |
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| Thermionic emission in semiconductors | |
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| Non-equilibrium carrier distributions | |
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| Drift and diffusion currents | |
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| Generation and recombination of electron-hole pairs in semiconductors | |
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| Solutions of typical transport equations in uniformly doped semiconductors | |
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| Further reading | |
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| Transport in inhomogeneous semiconductors | |
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| Properties of the pn junction at equilibrium | |
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| Current-voltage characteristics of the pn junction | |
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| The bipolar junction transistor | |
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| The junction field-effect transistor (JFET) | |
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| Semiconductor heterojunctions | |
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| Metal-semiconductor contacts and MESFET transistor | |
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| The metal-oxide-semiconductor structure and MOSFET transistor | |
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| Further reading | |
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| Electron gas in magnetic fields | |
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| Magnetization and magnetic susceptibility | |
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| Energy levels and density-of-states of a free-electron gas in magnetic fields | |
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| Energy levels of the two-dimensional electron gas in magnetic fields | |
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| Energy levels of the three-dimensional electron gas in magnetic fields | |
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| Orbital magnetic susceptibility and de Haas-van Alphen effect | |
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| Orbital magnetic susceptibility of a two-dimensional electron gas | |
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| Orbital magnetic susceptibility of a three-dimensional electron gas | |
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| Spin paramagnetism of a free-electron gas | |
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| Magnetoresistivity and classical Hall effect | |
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| The quantum Hall effect | |
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| Free energy of an electron gas in a uniform magnetic field | |
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| Generalized orbital magnetic susceptibility of the free-electron gas | |
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| Further reading | |
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| Magnetic properties of localized systems and Kondo impurities | |
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| Quantum mechanical treatment of magnetic susceptibility | |
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| Magnetic susceptibility of closed-shell systems | |
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| Permanent magnetic dipoles in atoms or ions with partially filled shells | |
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| Paramagnetism of localized magnetic moments | |
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| Localized magnetic states in normal metals | |
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| Dilute magnetic alloys and the resistance minimum phenomenon | |
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| Some phenomenological aspects | |
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| The resistance minimum phenomenon | |
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| Microscopic origin of the Kondo interaction: a molecular model | |
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| Magnetic impurity in normal metals at very low temperatures | |
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| Further reading | |
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| Magnetic ordering in crystals | |
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| Ferromagnetism and the Weiss molecular field | |
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| Microscopic origin of the coupling between localized magnetic moments | |
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| Antiferromagnetism in the mean field approximation | |
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| Spin waves and magnons in ferromagnetic crystals | |
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| The Ising model with the transfer matrix method | |
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| The Ising model with the renormalization group theory | |
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| The Stoner-Hubbard itinerant electron model for magnetism | |
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| Further reading | |
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| Superconductivity | |
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| Some phenomenological aspects of superconductors | |
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| The Cooper pair idea | |
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| Ground state for a superconductor in the BCS theory at zero temperature | |
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| Variational determination of the ground-state wavefunction | |
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| Ground-state energy and isotopic effect | |
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| Momentum distribution and coherence length | |
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| Excited states of superconductors at zero temperature | |
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| The Bogoliubov canonical transformation | |
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| Persistent currents in superconductors | |
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| Electron tunneling into superconductors | |
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| Treatment of superconductors at finite temperature and heat capacity | |
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| Diamagnetism of superconductors and Meissner effect | |
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| The phenomenological London model | |
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| Pippard electrodynamics and effective magnetic penetration depth | |
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| Macroscopic quantum phenomena | |
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| Order parameter in superconductors and Ginzburg-Landau theory | |
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| Magnetic flux quantization | |
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| Type-I and type-II superconductors | |
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| Cooper pair tunneling between superconductors and Josephson effects | |
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| The phonon-induced electron-electron interaction | |
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| Further reading | |
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| Subject index | |