Transport in superlattices on single layer graphene

TL;DR

This paper investigates how superlattice potentials affect electrical transport in undoped graphene, revealing that velocity anisotropy at Dirac points significantly influences conductivity, with new Dirac points forming under certain conditions.

Contribution

It introduces a combined continuum and tight-binding approach to analyze transport in graphene superlattices, highlighting the role of Dirac point anisotropy and the effects of different potential geometries.

Findings

Velocity anisotropy impacts conductivity significantly.

New Dirac points can be generated by 1D superlattice potentials.

Conductivity remains unchanged under certain 2D potentials without anisotropy.

Abstract

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.