Section outline

  • Effects of a weak perturbing potential (nearly free electrons): non degenerate case; degenerate case (two-levels system) (A&M, ch. 9; excluding The geometrical structure factor in monoatomic lattices with bases; Importance of spin-orbit splitting.)

    The tight-binding approach: introduction, general formulation; the simplified case of s-band arising from a single atomic s-level. Tight-binding in crystals with inversion symmetry; band dispersion.

    Exercises:

    1) weak potential: simple cases in 1D

    2) tight-binding: s-band arising from a 1D linear chain of atoms, density of states; s-band in 2D square lattice: band dispersion along some high symmetry directions, energy isosurfaces in the Brillouin zone, half filling of bands. (A&M, ch. 10)