Predicting the phonon spectra of coupled nonlinear chains using effective phonon theory

Abstract

In general one-dimensional nonlinear lattices, extensive studies have discovered the existence of renormalized phonons due to nonlinear interactions and found these renormalized phonons, as the energy carriers, are responsible for heat transport. Within the framework of renormalized phonons, a generic form of renormalized phonon spectrum has been derived and effective phonon theory (EPT) has been developed to explain the heat transport in general 1D nonlinear lattices. Our attention is dedicated to generalizing the EPT for two-layer nonlinear lattices and deriving the analytic expression of phonon spectra. By calculating the phonon spectra of different coupled models with EPT, it is found that the phonon dispersion relation is in good agreement with the result obtained from the spectral energy density method. It is demonstrated that the EPT of a coupled system can predict the phonon spectra of two-layer nonlinear lattices well. Thus, this finding may shed light on the prediction of heat conduction behavior in a coupled system, qualitatively, and provide a useful guide for designing thermal devices.