Intrinsic buckling strength of graphene: first-principles density functional theory calculations

Abstract

How graphene, an atomically thin two-dimensional crystal, explores the third spatial dimension by buckling under compression is not yet understood. Knowledge of graphene's buckling strength, the load at which it transforms from planar to buckled form, is a key to ensure mechanical stability of graphene-based nanoelectronic and nanocomposite devices. Here, we establish using first-principles theoretical analysis that graphene has an intrinsic rigidity against buckling, and it manifests in a weakly linear component in the dispersion of graphene's flexural acoustic mode, which is believed to be quadratic. Contrary to the expectation from the elastic plate theory, we predict within continuum analysis that a graphene monolayer of macroscopic size buckles at a nonzero critical compressive strain at T=0 K, and demonstrate it numerically from first principles. The origin of this rigidity is traced to the coupling between structural and electronic degrees of freedom arising from curvature-induced overlap between π orbitals in graphene.