6. Approximate treatment of electrons in a periodic potential: tight-binding approach (18 (1h), 20 Nov. 2024)
Section outline
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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.