Mechanical and acoustic properties of graphene and 2D membranes explained thanks to anharmonic effects*

The phonon properties of graphene, and in general of any 2D material, are still highly debated. The harmonic approximation predicts diverging atomic fluctuations and a constant linewidth of in-plane acoustic phonon modes at small momentum, which implies that graphene cannot propagate sound waves. The origin of these problems is the quadratic dispersion of the acoustic out-of-plane phonon frequencies obtained in the harmonic approximation. By including anharmonicity in a non-perturbative way within the Stochastic Self-Consistent Harmonic Approximation (SSCHA) we show that the physical dispersion expected experimentally for the acoustic out-of-plane mode should indeed be quadratic but actually compatible with well-defined sound waves. We verify this result using both atomistic simulations and a membrane model for graphene.

We also focus on the nature of the ripples by analyzing wihin the membrane model the scaling of the equal time out-of-plane correlation function. Our results replicate the crossover from classical correlations to quantum ones reported by Hašík et al. through quantum PIMC simulations.  We also suggest that most works in the membrane based literature are conditioned by the non-rotationally invariance of their model.

Our conclusions not only have a crucial role in the understanding of the mechanical and acoustic properties of graphene, but also of other strictly two-dimensional material.