Anharmonicity, phonon localization, two-phonon bound states, and vibrational spectra

Abstract

Neither local modes nor extended phonons precisely describe the excitations of anharmonic solids. A simple model Hamiltonian presented here characterizes the transition from local oscillator to optical phonon which would take place if one could continuously increase the phonon dispersion. The model is used to describe two types of transitions: a phonon-localization transition which is the analog of the Mott transition for electrons, and a spectral transition associated with the appearance of two-phonon bound states. In real materials, a sharp phonon-localization transition is probably not achievable, but striking spectral effects may be observable for some systems which are marginally able to produce two-phonon bound states.