Landau level splitting due to graphene superlattices

TL;DR

This paper investigates how graphene superlattices influence Landau level splitting under magnetic fields, revealing a lattice-specific effect where the zeroth Landau level splits, leading to a zero Hall conductivity plateau.

Contribution

It demonstrates a lattice-induced Landau level splitting in graphene superlattices that cannot be captured by continuum models, depending on superlattice orientation and magnetic field strength.

Findings

Zeroth Landau level splits into two sublevels for arm-chair oriented barriers.

Zero Hall conductivity plateau appears around the Dirac point.

Splitting persists even with disorder presence.

Abstract

The Landau level spectrum of graphene superlattices is studied using a tight-binding approach. We consider non-interacting particles moving on a hexagonal lattice with an additional one-dimensional superlattice made up of periodic square potential barriers, which are oriented along the zig-zag or along the arm-chair directions of graphene. In the presence of a perpendicular magnetic field, such systems can be described by a set of one-dimensional tight-binding equations, the Harper equations. The qualitative behavior of the energy spectrum with respect to the strength of the superlattice potential depends on the relation between the superlattice period and the magnetic length. When the potential barriers are oriented along the arm-chair direction of graphene, we find for strong magnetic fields that the zeroth Landau level of graphene splits into two well separated sublevels, if the width of the barriers is smaller than the magnetic length. In this situation, which persists even in the presence of disorder, a plateau with zero Hall conductivity can be observed around the Dirac point. This Landau level splitting is a true lattice effect that cannot be obtained from the generally used continuum Dirac-fermion model.