Anharmonicity of the acoustic modes of graphene

The anharmonicity of the acoustic phonon dispersion of graphene has been studied by the harmonic linear response (HLR) approach at finite temperature. This is a nonperturbative method based on the linear response of the system to applied forces, as derived from equilibrium computer simulations. Anharmonic shifts are analyzed in the long-wavelength limit at room temperature, with emphasis on the effect of applied tensile or compressive in-plane stress. The simulation results are compared with available analytical models, based either on first-order perturbation theory or on a description by anomalous exponents. The simulations show better agreement to the expectations of the perturbational approach. The effect of temperature and zero-point vibrations on the acoustic out-of-plane anharmonic shifts of graphene are briefly reviewed.