Vibrational excitations in lattices with anisotropic force-constant disorder analysed by the coherent potential approximation

Lattices with force-constant disorder are good model systems for studying vibrational excitations in disordered materials. Here, we investigate vibrations in a 2D square lattice, with anisotropic force-constant disorder, using the coherent potential approximation. The vibrational density of states is found analytically for low energy and disorder, and numerically otherwise, and these results are supported by precise numerical calculation using the kernel polynomial method.