Lattice Vibrations and Dispersion Relations near Conical Point in a Hexagonal Lattice

The dispersion relation of lattice vibrations in a hexagonal lattice is discussed on the basis of a simple model. It is found that there are the wavenumber-independent branches if only the nearest-neighbor interaction is taken into account. By taking the second-nearest-neighbor interaction into account, the origin of the appearance of the wavenumber-independent branches is clarified. At the reciprocal lattice point k = (1/3, 1/3, 0) of the hexagonal lattice, called the conical point, there are degenerate modes postulated from the symmetry, and the displacements of constituent atoms in them are concretely discussed.