Section outline

  • 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 (A&M, ch. 10).

    Bloch sums and their periodicity in direct space depending to k.

    Exercises: 

    - weak potential in 1D

    - tight-binding: s-band arising from a 1D linear chain of atoms, density of states; half filling of band.

    - tight-binding: s-band in 2D square lattice: band dispersion along some high symmetry directions, energy isosurfaces in the Brillouin zone.