Method to preserve the chiral-symmetry protection of the zeroth Landau level on a two-dimensional lattice

TL;DR

This paper presents a new lattice discretization method that preserves chiral symmetry and maintains the integrity of the zeroth Landau level in models of Dirac fermions on topological insulators under magnetic fields.

Contribution

It introduces a nonlocal discretization scheme that avoids chiral symmetry breaking and Landau level broadening caused by traditional Wilson fermions.

Findings

The Stacey discretization preserves chiral symmetry on the lattice.

The method prevents broadening of the zeroth Landau level under magnetic field fluctuations.

Spatial separation of opposite chirality states is effective in maintaining Landau level integrity.

Abstract

The spectrum of massless Dirac fermions on the surface of a topological insulator in a perpendicular magnetic field $B$ contains a $B$-independent "zeroth Landau level", protected by chiral symmetry. If the Dirac equation is discretized on a lattice by the method of "Wilson fermions", the chiral symmetry is broken and the zeroth Landau level is broadened when $B$ has spatial fluctuations. We show how this lattice artefact can be avoided starting from an alternative nonlocal discretization scheme introduced by Stacey. A key step is to spatially separate the states of opposite chirality in the zeroth Landau level, by adjoining $+B$ and $-B$ regions.