Effect of out-of-plane acoustic phonons on the thermal transport properties of graphene

The lattice thermal conductivity of graphene is evaluated using a microscopic model that takes into account the lattice's discrete nature and the phonon dispersion relation within the Brillouin zone. The Boltzmann transport equation is solved iteratively within the framework of three-phonon interactions without taking into account the four-phonon scattering process. The Umklapp and normal collisions are treated rigorously, thereby avoiding relaxation-time and long-wavelength approximations. The mechanisms of the failures of these approximations in predicting the thermal transport properties are discussed. Evaluation of the thermal conductivity is performed at different temperatures and frequencies and in different crystallite sizes. Reasonably good agreement with the experimental data is obtained. The calculation reveals a critical role of out-of-plane acoustic phonons in determining the thermal conductivity. The out-of-plane acoustic phonons contribute greatly and the longitudinal and transverse acoustic phonons make small contributions over a wide range of temperatures and frequencies. The out-of-plane acoustic phonons dominate the thermal conductivity due to their high density of states and restrictions governing the anharmonic phonon scattering. The selection rule severely restricts the phase space for out-of-plane phonon scattering due to reflection symmetry. The optical phonon contribution cannot be neglected at higher temperatures. Both Umklapp and normal processes must be taken into account in order to predict the phonon transport properties accurately.