Dispersion Relations near the Conical Point in Some Hexagonal Lattices

The dispersion relation in the hexagonal lattice is studied based on a simple model with the emphasis placed on the energy level crossing. By assuming the interactions between the nearest neighbors and second nearest neighbors, the analytical expression of the dispersion relation is shown. The level crossing at the Brillouin zone boundary is found to be due to the existence of the partial translation in the crystal structure. The appearance of the conical point crossing at the reciprocal lattice point k = (1/3, 1/3, 0) (the K-point) is reviewed from the group theoretical viewpoint.