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arXiv · 2210.01463

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

A. Donís Vela·G. Lemut·J. Tworzydło·C. W. J. Beenakker
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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.

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A. Donís Vela, G. Lemut, J. Tworzydło, C. W. J. Beenakker. 2022-10-04. Method to preserve the chiral-symmetry protection of the zeroth Landau level on a two-dimensional lattice. https://doi.org/10.1016/j.aop.2022.169208

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