FPL 085 Electron Theory of Solids

0/0 3/1

M. Divis, J. Masek

Recommended for diploma and PhD students.

Short and long range order. Crystal structure: point group symmetry and group of translations, space groups. Quasicrystals. Glasses and amorphous solids. Defects. Electron gas in solids. Results of Drude-Lorentz theory. Reciprocal space. Bloch theorem. Bloch functions. Brillouin zone-reduced, extended, periodic scheme. k-p method. Effective mass approximation. Wannier theorem. Density of states & resolvent (Green function). Nearly free electron approach (NFE). Linear Combination of Atomic Orbitals (LCAO) approach, minimal basis, Harrison scheme. Kronig-Penney model. Density Functional Theory (DFT) versus Hartree-Fock approximation (HF), methods: Linear Augmented Plane Wave (LAPW), Optimized LCAO. 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. Electron liquid-perturbation theory: HFA, Luttinger theorem, Feynmann diagrams. Strong coupling: Anderson gas with n>0, n<0. Creation of local magnetic moment (single impurity Anderson model). Hubbard model. Stoner theory of ferromagnetism. Disordered local moment picture of paramagnetism. Heisenberg Hamiltonian. Linear response. Kubo formula. Electrical conductivity. Optical transition&Optical constants. Kramers-Kronig relations. Photoemission.