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Department of Physics

18101

18101  Electronic Structure and Properties of Matter    

Course Webpage: https://eclass.uoa.gr/courses/PHYS108

Course Content

  • Description of interacting electrons in solids: Introduction. Rayleigh-Ritz variational principle. Hartree and Hartree-Fock methods. Koopmans theorem. Exchange hole. Hartree-Fock approximation for free electrons. Χ-α potential. Spin polarization of the homogeneous electron gas. Density functional theory. Kohn-Sham equations. Local density approximation. Meaning of the single-electron eigenvalues. Lifetime of excited states.
  • Elements of group theory: Definition of a point group. Representations of groups. Conjugate elements and classes. Orthogonality of irreducible representations. Projection operators. Solution of Schrödinger’s equation. Direct product representation. Selection rules. The continuous group of rotations in three dimensions. Lifting of symmetry-induced degeneracy by a perturbation. Crystallographic point groups. Space groups.
  • Electron states in crystals: Bloch’s theorem. Symmetry of Bloch states. Energy bands. The plane wave method. Density of states. High symmetry points and lines in the first Brillouin zone. Symmetry classification of energy bands.
  • Electronic structure of metals, semiconductors, insulators: Metals, semiconductors and insulators. Electronic structure of simple metals. The method of linear combination of atomic orbitals. First-principles methods, transition metals. Ferromagnetic metals. Semiconductors.
  • Point defects: Green’s function. Lippmann-Schwinger equation. Dispersion relations. Transition matrix, Dyson’s equation. Free electron and tight binding Green’s functions. Defect states in crystals. Localized defect states in simple metals. Electronic structure of defects in simple metals.
  • Disordered materials: Types of disorder. Study of a one-dimensional alloy. Self-energy. Virtual crystal approximation. Average T-matrix approximation. Coherent potential approximation. Localization due to disorder. Thermal hopping conductivity.
  • Surfaces: The structure of surfaces. Potential in the vicinity of a surface – electron emission. Complex band structure. Electron states in a semi-infinite crystal.