As we know, there are two distinct Dirac points for the free electrons in graphene. Which means that the energy spectrum of the 2$\times$2 Hermitian matrix $H(k_x,k_y)$ 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 $k_x,k_y$ 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