Improved scaling rules for bandgaps in graphene nanomeshs

The ways to solve an outstanding problem on how to properly pattern graphene to induce bandgaps are reported, in particular, related altering regularities and mechanisms are investigated systematically. For the graphene nanomeshes (GNMs) with circular, triangular and rectangular holes, the respective new scaling rules to quantitatively reflect the relationship between the bandgap and the structural parameters of GNMs are proposed, which demonstrates a well applicability for a description of bandgaps of GNM with different size, shape, and density of hole. Furthermore, the underlying mechanisms for opening bandgap are revealed and the altering regularities of bandgaps are clearly explained.