Induced chiral Dirac fermions in graphene by a periodically modulated magnetic field

TL;DR

Applying a periodically modulated magnetic field to graphene induces new Dirac points, preserves the Dirac cone structure, and results in unique Landau level degeneracies and quantized Hall conductivity steps.

Contribution

This paper demonstrates that a staggered magnetic field can generate and manipulate Dirac points in graphene without destroying its electronic structure.

Findings

New Dirac points are generated and can be controlled by the magnetic field.

The zeroth Landau level exhibits a robust 4n_t-fold degeneracy.

Hall conductivity shows quantized steps of size 4n_t e^2/h.

Abstract

The effect of a modulated magnetic field on the electronic structure of neutral graphene is examined in this paper. It is found that application of a small staggered modulated magnetic field does not destroy the Dirac-cone structure of graphene and so preserves its 4-fold zero-energy degeneracy. The original Dirac points (DPs) are just shifted to other positions in k space. By varying the staggered field gradually, new DPs with exactly the same electron-hole crossing energy as that of the original DPs, are generated, and both the new and original DPs are moving continuously. Once two DPs are shifted to the same position, they annihilate each other and vanish. The process of generation and evolution of these DPs with the staggered field is found to have a very interesting patten, which is examined carefully. Generally, there exists a corresponding branch of anisotropic massless fermions for each pair of DPs, resulting in that each Landau level (LL) is still 4-fold degenerate except the zeroth LL which has a robust $4n_t$-fold degeneracy with nt the number of pairs of DPs. As a result, the Hall conductivity $\sigma_{xy}$ shows a step of size $4n_te^2/h$ across zero energy.