As we know, there are two distinct Dirac points for the free electrons in graphene. Which means that the energy spectrum of the 2×2 Hermitian matrix H(kx,ky) has two degenerate points K and K′ in BZ.
According to the von Neumann-Wigner theorem (no-crossing theorem): To make two eigenvalues of a Hermitian matrix (depending on some independent real parameters) cross, generally speaking, we need to change at least 3 parameters. But in the 2D graphene case, the variation of only 2 parameters kx,ky can cause the energy levels cross.
So I want to know whether there are some physical or mathematical reasons for the existence of Dirac points in graphene.
This post imported from StackExchange Physics at 2014-03-09 08:46 (UCT), posted by SE-user K-boy