Perturbation theory for weakly coupled two-dimensional layers

A key issue in two-dimensional structures composed of atom-thick sheets of electronic materials is the dependence of the properties of the combined system on the features of its parts. Here, we introduce a simple framework for the study of the electronic structure of commensurate and incommensurate layered assemblies based on perturbation theory. Within this framework, we calculate the band structure of commensurate and twisted bilayers of graphene (Gr) and of a Gr/h-BN heterostructure, which we compare with reference full-scale density functional theory calculations. This study presents a general methodology for computationally efficient calculations of two-dimensional materials and also demonstrates that for relatively large twist in the graphene bilayer the perturbation of electronic states near the Fermi level is negligible.