Syllabus
* One electron approximation
Adiabatic approximation, one electron crystal potential, direct and reciprocal lattice, Bloch theorem, consequences. Brillouin zones. NFE and TB methods. Born-Karman conditions, efective mass, electron-hole symmetry, metal-semiconductor-isolator, Fermi surface, real electron structure in 3, 2 and 1 dimensions.
* Consequences of translational symmetry breaking
Wannier theorem, impurity and surface states, superlattices and quantum structures.
* Quantization of physical fields
Lattice vibrations, harmonic approximation, normal coordinates, acustic and optical phonons, representation of occupation numbers.
* Thermodynamics and statistical physics of elementary excitations
Specific heat of electron gas and phonons, statistic of semiconductors with impurity states (Einstein and Debye models), anharmonicity, thermal expansion.
* Electron in electric and magnetic fields
Classical and quantum motion. Landau levels, cyclotron frequency, orbit topology, de Hass-van Alphen effect.
* Dialecrtric properties of solids
General dialectric constant, dispersion, local and macroscopic fields, jellium, screening, Thomas-Fermi model, screening of the impurity, Friedel oscillations,
Lyddane-Sachs-Teller expression.
* Quasiparticles in solids
Perturbation theory, canonical transformation, Green functions.
Excitons, magnons, plasmons, polarons, BCS theory of superconductivity.
Annotation
Physical properties of solids. Influence of translation symmetry and its distorsion by external fields and internal perturbations.
Lattics vibrations are used to show a quantization of physical fields. Quasiparticles (excitons, magnons, plasmons, polarons) are introduced.
Application of the perturbation theory methods, canonical transformations, and Green functions to the electron-phonon interaction is used for investigation of their mutual interaction.