Consider a 2D tight-binding band on a square lattice with dispersion relation: E(k) =-2tcos(ka) + cos(kya. A) Draw the Fermi surface roughly for an electron density of n = 1/5a² and n = 9/5a². Show by scratching which portion of the Brillouin zone is inside the Fermi sea and which part is outside. B) Estimate the density of states at the Fermi energy, D(2EF) as a function of the electron density per unit cell in the limit of a nearly empty or nearly filled band, expressing your result in terms of the density n.