I've been doing simulations of band structure for 2D optical lattices, and something I've noticed is that, for sufficiently shallow lattices, there are typically points on the edge of the first Brillouin zone where the lowest bands touch (or nearly touch). These smell like Dirac points, though I don't know this rigorously.
My question is: Is there an analytical argument why Dirac points should be the norm for 2D lattices? If so, what can be said analytically about the location of these points?
