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

TL;DR

This paper demonstrates a method to protect the zeroth Landau level in a 2D lattice by using boundary conditions and a special discretization, avoiding the need to double system size.

Contribution

It introduces a boundary-condition approach combined with tangent fermion discretization to preserve chiral symmetry and protect the zeroth Landau level without enlarging the system.

Findings

Achieves zeroth Landau level protection without system doubling.

Uses boundary conditions to isolate chiral states.

Employs tangent fermion discretization for Dirac equation.

Abstract

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.