Landau Levels and Quantum Hall Effect in Graphene Superlattices

TL;DR

This paper demonstrates that applying a one-dimensional periodic potential to graphene creates new zero-energy fermion branches, leading to modified Landau levels and Hall conductivity steps, revealing unique electronic properties of graphene superlattices.

Contribution

It introduces a theoretical framework showing how external periodic potentials generate additional massless fermions and alter quantum Hall effects in graphene.

Findings

Additional zero-energy fermion branches are generated.

Landau level degeneracy becomes 4(2N+1)-fold.

Hall conductivity exhibits steps of size 4(2N+1)e^2/h.

Abstract

We show that, when graphene is subjected to an appropriate one-dimensional external periodic potential, additional branches of massless fermions are generated with nearly the same electron-hole crossing energy as that at the original Dirac point of graphene. Because of these new zero-energy branches, the Landau levels at charge neutral filling becomes 4(2N+1)-fold degenerate (with N=0,1,2,..., tunable by the potential strength and periodicity) with the corresponding Hall conductivity $\sigma_{xy}$ showing a step of size 4(2N+1)$e^2/h$. These theoretical findings are robust against variations in the details of the external potential and provide measurable signatures of the unusual electronic structure of graphene superlattices.