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**1. Homework Statement**

Given some dispersion relation for the tight binding approximation in 2D:

e(k_x,k_y) = -2t_1[cos(k_x*a)+cos(k_y*a)]-4t_2[cos(k_x*a)cos(k_y*a)]

Show that the density of states has a logarithmic singularity for some choice of parameters t_i.

**2. Homework Equations**

g(e)de=g integral dS/(2*pi)^3 *1/|grad e(K)|

**3. The Attempt at a Solution**

When it says logaritmic singularity is it referring to von hove singularity?

First I expanded the cosines.

-2t_1[2-k_x^2*a^2/2 -k_y^2*a^2/2] -4t_2[1+k_x^2*a^2 k_y^2*a^2

Then what do I do?