Let us say we have the 2D graph of $E(k_1,k_2)$ for two atom nn hopping hamiltonian and somehow we find that there are zero gap at the corners of Brillouin zone (which I don't really see how they are related). Now the question asks how could this be, how could we have zero gaps at the corners of the Brillouin zone?
I don't understand the question; why is it that we are not supposed to have zero gaps at the corners of Brillouin zone?
I mean isn't Brillouin zone just the Wigner-Seitz cell but in reciprocal lattice space? What does it has to do with gap and how can we relate the $E(k_1,k_2)$ graph to Brillouin zone?
