Transport in superlattices on single-layer graphene

We study transport in undoped graphene in the presence of a superlattice potential both within a simple continuum model and using numerical tight-binding calculations. The continuum model demonstrates that the conductivity of the system is primarily impacted by the velocity anisotropy that the Dirac points of graphene develop due to the potential. For one-dimensional superlattice potentials, new Dirac points may be generated, and the resulting conductivities can be approximately described by the anisotropic conductivities associated with each Dirac point. Tight-binding calculations demonstrate that this simple model is quantitatively correct for a single Dirac point, and that it works qualitatively when there are multiple Dirac points. Remarkably, for a two-dimensional potential which may be very strong but introduces no anisotropy in the Dirac point, the conductivity of the system remains essentially the same as when no external potential is present.