Electronic spectrum and tunneling current in curved graphene nanoribbons

Starting with the Dirac equation in a curved space–time, applied for the description of the long-wave electrons in curved graphene nanoribbons, we calculated the electronic spectrum and the density of states. Based on the derived density of states we were able to compute the IVIV-characteristics of a nanoribbon–metal tunnel junction. The dependence on the geometric characteristics of a nanoribbon is revealed.

► The effective equation describing the electrons in a curved graphene is derived.
► Our study confirms the significant influence of geometry on the properties of nanostructures.
► IVIV characteristics for a curved graphene–metal is similar to the one for classical diodes.