FPL061

1. Fundamental questions in the theory of solids.

Phenomenological and microscopic approaches. Types of binding forces and structure of solids. Description of symmetry of crystalline solids. Adiabatic approximation in the study of motion of electrons and nuclei.

2. Vibrations of crystal lattice and its thermal properties.

Harmonic approximation and normal vibrations of crystalline solids. Acoustic and optical branches of vibrations of ions in crystals, vibration spectrum of real crystals. Phonons as quasiparticles in the systém of collectively vibrating ions in crystals. Specific heat of solids.

3. Electron theory of ideal crystalline solids.

The Hartree - Fock approximation of self - consistent field. Bloch theory of motion of electrons in a periodic electric field in the crystal. Properties of wave functions and of energy spectrum, quasimomentum of itinerant electrons, the approximation of effective mass. Positive holes in an almost completely filled electron bands.

4. Methods of calculation of band electron structure of solids.

The approximation of nearly free electrons, the method of tightly bound electrons, the augmented plane wave and orthogonalized plane wave methods, the pseudopotential method. Band structure of various types of solids.Fermi surfaces of energy of itinerant electrons in metals. Properties of electrons in valence and conduction bands in semiconductors.

5. Electron theory of real solids.

Wannier theory of motion of electron in perturbed periodic electric field. Localized states of itinerant electrons in crystals with imperfections. States of electrons near of surface of solids and in thin films. Donor and acceptor energy levels of impurities in semiconductors. Excitons. States of electrons in disordered solids.

6. Electric, magnetic and optical properties of solids.

Properties of ensemble of itinerant electrons in statistical equilibrium. Dynamics of itinerant electrons in external electric and magnetic fields. Paramagnetism and diamagnetism of itinerant electrons. Interband and intraband optical transitions.

7. Transport phenomena in solids.

Boltzmann kinetic equation. Scattering of itinerant electrons by phonons and impurities. Relaxation time of conduction electrons in metals and semiconductors. Galvanomagnetic, thermoelectric and photoelectric phenomena.