Electronic states in a superlattice consisting of alternating strips of single-layer and bilayer graphene

A model of a superlattice consisting of alternating strips of single-layer and bilayer graphene is proposed, whose parameters of the energy spectrum can be controlled by changing the external electric field perpendicular to the surface of the sample. Using the Kronig-Penney model, the dispersion equation is obtained, based on the analysis of which the energy spectrum of a graphene superlattice is studied depending on the ratio of the strip widths of single-layer and bilayer graphene. The results of the analytical solution are compared with the results of modeling by methods of the theory of the density functional. It is shown that the low-energy approximation used to derive the dispersion equation is valid when considering a superlattice with narrow strips of bilayer graphene and wide strips of single-layer graphene.