4. Independent electrons in a periodic potential: general aspects (25,26,27 Oct; 8,9,10 Nov 2023)
Section outline
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Periodic potential: Bloch theorem, I and II proof (Ch. 8). [25 Oct.]
Consequences of the Block theorem: crystalline momentum; velocity; energy bands. (Ch. 8) [26 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)
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 + Ch. 9]. [27 Oct.]Divergences in the DOS integrals - Van Hove singularities in 1D, 2D, 3D. Exercise n. 2 Ch. 8 of A&M [6 Nov.]"Empty lattice" band structure in 1D and 2D (square lattice) + other exercised [8, 9 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 [10 Nov., I part of the lecture]Bloch sums and their periodicity in direct space depending to k. Calculation of k_F in the "empty lattice" model and comparison of the Fermi surface with the Brillouin zone [10 Nov.- II part]