Boundary-condition-assisted chiral-symmetry protection of the zeroth Landau level on a two-dimensional lattice

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Vela, A. Donís, Beenakker, C. W. J.
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866912501943238656
author Vela, A. Donís
Beenakker, C. W. J.
author_facet Vela, A. Donís
Beenakker, C. W. J.
contents The massless two-dimensional Dirac equation in a perpendicular magnetic field B supports a B-independent "zeroth Landau level", a dispersionless zero-energy-mode protected by chiral symmetry. On a lattice the zero-mode becomes doubly degenerate with states of opposite chirality, which removes the protection and allows for a broadening when the magnetic field is non-uniform. It is known that this fundamental obstruction can be avoided by spatially separating the doubly degenerate states, adjoining +B and -B regions in a system of twice the size. Here we show that the same objective can be achieved without doubling the system size. The key ingredients are 1) a chirality-preserving "tangent fermion" discretization of the Dirac equation; and 2) a boundary condition that ensures the zero-mode contains only states of a single chirality.
format Preprint
id arxiv_https___arxiv_org_abs_2505_13658
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Boundary-condition-assisted chiral-symmetry protection of the zeroth Landau level on a two-dimensional lattice
Vela, A. Donís
Beenakker, C. W. J.
Mesoscale and Nanoscale Physics
The massless two-dimensional Dirac equation in a perpendicular magnetic field B supports a B-independent "zeroth Landau level", a dispersionless zero-energy-mode protected by chiral symmetry. On a lattice the zero-mode becomes doubly degenerate with states of opposite chirality, which removes the protection and allows for a broadening when the magnetic field is non-uniform. It is known that this fundamental obstruction can be avoided by spatially separating the doubly degenerate states, adjoining +B and -B regions in a system of twice the size. Here we show that the same objective can be achieved without doubling the system size. The key ingredients are 1) a chirality-preserving "tangent fermion" discretization of the Dirac equation; and 2) a boundary condition that ensures the zero-mode contains only states of a single chirality.
title Boundary-condition-assisted chiral-symmetry protection of the zeroth Landau level on a two-dimensional lattice
topic Mesoscale and Nanoscale Physics
url https://arxiv.org/abs/2505.13658