Calculation of Phonon-Phonon Interactions and the Absence of Two-Phonon Bound States in Diamond

Abstract

We demonstrate that anharmonic phonon-phonon coupling constants can be extracted from frozen-phonon total-energy calculations. The method is applied to the optical modes of diamond. The zone-center coupling constants are completely determined through fourth order, and are used to compute an effective four-phonon vertex including virtual optical-phonon exchange. The interaction is found to have the wrong sign to allow formation of a two-phonon bound state.