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.

Contribution to a special issue of Annals of Physics in memory of Kostya Efetov

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Cited by in corpus (3)

• Tangent fermions: Dirac or Majorana fermions on a lattice without fermion doubling
• Single-cone Dirac edge states on a lattice
• Boundary-condition-assisted chiral-symmetry protection of the zeroth Landau level on a two-dimensional lattice