Why Dirac points in graphene are where they are?

Abstract

We present a simple group theory explanation of the fact that the energy bands merge in the corners of the Brillouin zone for graphene and for two particular cases of Kagome lattice for arbitrary tight--binding Hamiltonian. We connect the linearity of the spectrum in the vicinity of these points for monolayer graphene, bilayer graphene for AA stacking and Kagome lattice with the properties of the conical points of the surface, known from geometry.