Flexural phonons and thermal transport in multilayer graphene and graphite

Abstract

We present a theory for the lattice thermal conductivity ${\ensuremath{\kappa}}_{L}$ of multilayer graphene (MLG) and graphite, which is based on an exact numerical solution of the Boltzmann equation for phonons. Dominant contributions to ${\ensuremath{\kappa}}_{L}$ from out-of-plane or flexural phonons are found, which is consistent with previous findings for single-layer graphene (SLG). However, the interaction between graphene layers in MLG and graphite breaks a selection rule on phonon-phonon scattering, causing their ${\ensuremath{\kappa}}_{L}$s to be much lower than that of SLG. ${\mathrm{C}}^{13}$ isotopes are shown to be an important scattering mechanism, accounting for an \ensuremath{\sim}15% additional drop in the ${\ensuremath{\kappa}}_{L}$ of these systems. We demonstrate that the ${\ensuremath{\kappa}}_{L}$ values converge to that of graphite after only about five layers, a consequence of weak interlayer coupling. These findings are qualitatively consistent with recent measurements of ${\ensuremath{\kappa}}_{L}$ for MLG.