4. Independent electrons in a periodic potential: general aspects (21 (1h), 23 (1h), 28 (1h), 30 Oct.; 4, 6 Nov. 2024)
Section outline
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Periodic potential: Bloch theorem, I [21 Oct.] and II [23 Oct.] proof (Ch. 8).
Consequences of the Block theorem: crystalline momentum; velocity; energy bands. (Ch. 8) [28 Oct.]
Fermi surfaces. Density of states (DoS): different approaches. Derivation of the DoS using the properties of the delta-function . Van Hove singularities. (Ch. 8) [30 Oct.]
Brillouin zones, band folding and band indices, band plots in reduced zone / periodic / extended representation Fermi surfaces and their folding into the first Brillouin zone (end of Ch. 8]. [30 Oct.]Divergences in the DOS integrals - Van Hove singularities in 1D, 2D, 3D. Exercise n. 2 Ch. 8 of A&M [4 Nov.]"Empty lattice" band structure in 1D and FCC [4 Nov.]
A nice applet for plotting the "empty lattice" bands: PHY.K02UF Molecular and Solid State Physicshttp://lampx.tugraz.at/~hadley/ss1/emfield/empty/empty.phpComments on selected slides on: band structures, Fermi surfaces, DOS [6 Nov.]Calculation of k_F in the "empty lattice" model and comparison of the Fermi surface with the Brillouin zone [6 Nov.]