Problem: Conductivity of Tight-Binding Band

        Consider a two-dimensional metal with a square lattice of lattice spacing a. The conduction band is described by the tight-binding approximation,

 

and the relaxation time is independent of the electron momentum or energy. The band is half-filled.

(a) Using the solution of the Boltzmann equation, calculate the conductivity tensor.

(b) Compare the result of (a) to the conductivity from the Drude model. (Use the same electron density and relaxation time. What is the relevant effective mass?)