Flat dispersion relations of phonons

摘要

We propose a constructive method of designing a new class of crystalline solids in which the phonons have flat dispersion relations in the entire or partial k -space. This method is based on a new theory of flat bands recently proposed by Nishino, Goda and Kusakabe for discussing electronic systems. By applying it to phonons, we can design flat dispersion relations almost as we want assuming we can control the values of force constants.