Simulation of Heat Transport in Graphene Nanoribbons Using the Ab-Initio Scattering Operator

Abstract

We present a deviational Monte Carlo method for simulating phonon transport in graphene using the ab initio 3-phonon scattering operator. This operator replaces the commonly used relaxation-time approximation, which is known to neglect, among other things, coupling between out of equilibrium states that are particularly important in graphene. Phonon dispersion relations and transition rates are obtained from density functional theory calculations. The proposed method provides, for the first time, means for obtaining solutions of the Boltzmann transport equation with ab initio scattering for time- and spatially-dependent problems. The deviational formulation ensures that simulations are computationally feasible for arbitrarily small temperature differences; within this formulation, the ab initio scattering operator is treated using an efficient stochastic algorithm which, in the limit of large number of states, outperforms the more traditional deterministic methods used in solutions of the homogeneous Boltzmann equation. We use the proposed method to study heat transport in graphene ribbons.