Phonon scattering in one-dimensional anharmonic crystals and superlattices: Analytical and numerical study

Second-order perturbation theory based on multiple time scale analysis is used to illuminate three-phonon scattering processes in the one-dimensional anharmonic monoatomic crystal. Molecular dynamics simulation techniques in conjunction with spectral energy density analyses are used to quantify phonon mode lifetime in (1) the monoatomic crystal and (2) a series of superlattice configurations. It is found that the lifetime of vibrational modes in the monoatomic crystal is inherently long, because the conditions for conservation of wave vector and frequency are pathologically difficult to satisfy. Superlattice configurations, however, offer band-folding effects, whereby the availability of phonon decay channels decreases the lifetime of the vibrational modes supported by the medium.