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 contains a -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 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 and regions.