Graphene as a Strictly 2D Sheet or as a Film of Small but Finite Thickness

Abstract

We study an interface between two media separated by a strictly 2D sheet. We show how the amplitude reflection coefficient can be modeled by that for an interface where the 2D sheet has been replaced by a film of small but finite thickness. We give the relationship between the 3D dielectric function of the thin film and the 2D dielectric function of the sheet. We apply this to graphene and show how the van der Waals interaction between two graphene sheets is modified when going from the 2D sheet description to the thin film description. We also show the wrong result from keeping the 2D dielectric function to represent the film medium.