Tight-binding theory of graphene bending

Abstract

We model bent graphene as a large-radius (g1 nm) single-walled carbon nanotube in order to uncover the origin of its bending rigidity. An analytic formula based on the H\uckel molecular orbital theory connects the finite resistance to bending directly to the curvature-induced torsional misalignment of the $\ensuremath{\pi}$ orbitals no longer of pure $p$ character. The analytical predictions are supported by direct density functional theory-based tight-binding objective molecular dynamics calculations. Our tight-binding theory also gives useful insight into modeling graphene bending with continuum plate mechanics and classical interatomic potentials.