Syllabus
FPL143
Electron gas in solids. Results of Drude-Lorentz theory.
Bloch theorem. Bloch functions. Reciprocal space. Brillouin zone. 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. Density Functional Theory versus Hartree-Fock approximation.
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).
Electrical conductivity. Linear response. Optical transition&Optical constants. Kramers-Kronig relations. Photoemission (XPES, BIS).
Specific heat. Phonons. Debye and Einstein models. Anharmonic corrections.
Models for localized magnetic moments: Weiss molecular field model, Heisenberg and Izing model, crystal field theory. Models for delocalized magnetic moments: Stoner model of itinerant electron magnetism, Landau theory of weakly itinerant electron ferromagnetism, the linearized spin-fluctuation model, comparison.
Point defects: shallow impurities, deep impurities. Mixed crystals: Virtual Crystal Approximation (VCA) versus split band case, Green functions, Coherent Potential Approximation (CPA). Spectral density.
Annotation
Conduction electrons in materials (classical and quantum description), electrons in periodic potential. Electronic structure of metals, semiconductors and insulators.
Transport and thermal properties, optical and magnetic properties of materials. Examples of real materials.