Flexural phonons and thermal transport in graphene

We show through an exact numerical solution of the phonon Boltzmann equation that the lattice thermal conductivity of graphene is dominated by contributions from the out-of-plane or flexural phonon modes, previously thought to be negligible. We connect this unexpected result to the anomalously large density of states of flexural phonons compared to their in-plane counterparts and to a symmetry-based selection rule that significantly restricts anharmonic phonon-phonon scattering of the flexural modes. The result is found to hold in the presence of the ripples known to occur in graphene, phonon-isotopic impurity scattering, and rigidity of the flexural phonon branch arising from the long-wavelength coupling between flexural and in-plane modes. Finally, accurate inclusion of the momentum conserving Normal phonon-phonon scattering processes within the context of a full solution of the phonon Boltzmann equation are shown to be essential in accurately describing the graphene thermal conductivity, in contrast to the more commonly used relaxation time and long wavelength approximations.