Electronic superlattices in corrugated graphene

We theoretically investigate electron transport through corrugated graphene ribbons and show how the ribbon curvature leads to an electronic superlattice with a period set by the corrugation wavelength. Transport through the ribbon depends sensitively on the superlattice band structure which, in turn, strongly depends on the geometry of the deformed sheet. In particular, we find that for ribbon widths where the transverse level separation is comparable to the band edge energy, a strong current switching occurs as a function of an applied back gate voltage. Thus, artificially corrugated graphene sheets or ribbons can be used for the study of Dirac fermions in periodic potentials. Furthermore, this provides an additional design degree of freedom for graphene-based electronics.