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

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.