Syllabus
1. Crystal structure
2. Long-range and short-range order. Crystal structure: translational and point groups of symmetry, space groups. Amorphous solids, glasses. Defects.
3. Quantum description of an ideal crystal
4. Hamiltonian for a motion of electrons and nuclei. Born-Oppenheimer approximation.
5. Basic features of electronic structure
6. Bloch theorem, Bloch functions. Reciprocal space. Brillouin zone. Electron gas in condensed state. Results of Drude-Lorent theory. Reduced, extended and periodic scheme of electron structure. k-p method. Effective mass approximation (quasiparticles). Wannier functions. Density of states, Green's function.
7. Electron states in crystals
8. Kronig-Penney model. Nearly free electron approximation. Linear combination of atomic orbitals (LCAO), minimal base, Harrison method of tight binding.
9. Electron structure calculation methods
10. Density functional theory (DFT) versus Hartree-Fock (HF) approximation. Methods: Linear augmented plane waves (LAPW), optimized LCAO, pseudopotentials.
11. Typical examples of band structures
12. Chemical bonding. Metals, semi-metals, semiconductors with direct and indirect electron gap, insulators. Special groups of solids - chemical trends: transitive metals (d- and conduction electron hybridization), cubic semiconductors (hybridization gap, ionic behavior effects).
13. Phonons in condensed state
14. Lattice vibrations. Occupational numbers representation. Relation phonons- thermal capacity and phonons-thermal conductivity. Electron-phonon interaction and its consequences. Phonons in BCS-theory of super-conductivity.
15. Electronic structure of real solids (with defects)
16. Green functions. Point defects. Mixed crystals: virtual crystal approximation (VCA), coherent potential approximation (CPA). Spectral density.
17. Electron correlation
18. Failures of one-electron approximation. Pair distribution function. Correlation in frame of DTF (local density approximation (LDA)). Extending of LDA: generalized gradient approximation (GGA), self-interaction correction (SIC). Hubbard model (LDA+U).
19. Optical, transport and magnetic properties
20. Linear response theory. Kubo's formula. Electrical conductivity. Optical transitions and optical constants. Kramers-Kronig relations. Photoemission (XPES, BIS). Stoner theory of itinerant magnetism.
Annotation
Quantum model of a crystal. Physical properties of the lattice. Band model of solids.
Effect of external fields. Optical and transport properties.