Syllabus
FPL085
Short and long range order. Crystal structure: transitional and point group symmetry, space groups. Amorphous solids and glasses. Defects. Bloch theorem. Bloch functions. Reciprocal space. Brillouin zone. Electron gas in solids. Results of Drude-Lorentz theory. Reduced, extended, periodic scheme. k-p method. Effective mass approximation (Quasiparticles). Wannier theorem. Wannier functions. Density of states & resolvent (Green function). Kronig-Penney model. Nearly free electron approach (NFE). Linear Combination of Atomic Orbitals (LCAO) approach, minimal basis, Harrison scheme. Density Functional Theory (DFT) versus Hartree-Fock approximation (HF). Methods: Linear Augmented Plane Wave (LAPW), optimized LCAO and local orbitals (FPLO), pseudopotentials. Chemical bond. Metals, semimetals, direct- and indirect-gap semiconductors, insulators. Special groups of solids - chemical trends: transition metals (hybridized d- and conduction states), tetrahedral semiconductors (hybridization gap, effects due to ionicity)
.Green functions. Point defects: shallow impurities, Anderson and Koster-Slater model for deep levels. Mixed crystals: Virtual Crystal Approximation (VCA) versus split band case, Coherent Potential Approximation (CPA). Spectral density. Shortcomings of the independent-electron approximation. Pair distribution function. Unrestricted SCF approximation, Correlations in DFT (LDA). Extensions of LDA: GGA, SIC, GW. Hubbard model (LDA+U). Models for localized moments: Weiss molecular field model, Heisenberg and Izing model, Crystal field theory. Models for delocalized moments: Stoner model of itinerant electron magnetism. Landau theory of weakly itinerant electron ferromagnetism, the linearized spin-fluctuation model, comparison. Linear response. Kubo formula. Electrical conductivity. Optical transition&Optical constants. Kramers-Kronig relations. Photoemission (XPES, BIS).
Annotation
Atomic structure and chemical bond. Basic properties of electronic structure of condensed matter.
Band structure of materials and methods of its calculation. Admixtures, perturbations and alloys.
Electron-electron and electron-phonon interaction. Itinerant magnetism.
Electron transport. Optical transitions.