Anharmonic Renormalization Of The Dispersion Of Flexural Modes In Graphene Using Atomistic Calculations

We investigate through an atomistic method the effects of anharmonicity on the dispersion of flexural modes of graphene. Using a calculation based on ensemble averages of correlations among displacements and forces, we calculate the temperature-dependent frequencies for a semiempirical potential for graphene. We find that the dispersion relation of the flexural modes of graphene is renormalized by anharmonic coupling to other modes. Our calculations confirm that the anharmonic continuum results of Mariani and von Oppen [Phys. Rev. Lett. 100, 076801 (2008)] hold in detail for small wave number and at low temperatures. We examine the deviation from the continuum result outside of that range.