513.001 Molecular and Solid State Physics

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Tight binding model

In the tight-binding model for a bcc lattice, the dispersion relationship for one of the electron bands is,

$\large E=\epsilon - 8t\cos\left(\frac{k_xa}{2}\right)\cos\left(\frac{k_ya}{2}\right)\cos\left(\frac{k_za}{2}\right).$

(a) What is the effective mass of electrons near the Γ point $(k = 0)$?

(b) There is one electron per unit cell in this band. Is this material a metal, a semiconductor, or an insulator? Explain your reasoning.

(c) The dispersion relation above is only for one band. A real material has many bands. How do you calculate more bands using the tight binding model?