Scaling law for energy bandgap and effective electron mass in graphene nano mesh

Abstract

For the energy bandgap of semiconducting graphene nano mesh (GNM), chirality dependent scaling rules have been proposed so far. Based on extensive tight binding studies and simple geometric arguments, we report that Pedersen scaling governs not only the energy bandgap but also the effective mass of the Bloch electron of the semiconducting GNM regardless of its chirality or the crystallography of the mesh holes when the hole areal fraction is low.