Single-cone Dirac edge states on a lattice

TL;DR

This paper demonstrates how to simulate Dirac edge states on a 2D lattice, effectively modeling boundary states of topological insulators without fermion doubling issues.

Contribution

It introduces a lattice discretization method that accurately reproduces Dirac edge states on a finite lattice, overcoming fermion doubling problems.

Findings

Successfully simulates Dirac edge states on a lattice

Adapts tangent fermion discretization for lattice termination

Provides a framework for lattice modeling of topological insulator boundaries

Abstract

The stationary Dirac equation $(p\cdot\sigma)\psi=E\psi$, confined to a two-dimensional (2D) region, supports states propagating along the boundary and decaying exponentially away from the boundary. These edge states appear on the 2D surface of a 3D topological insulator, where massless fermionic quasiparticles are governed by the Dirac equation and confined by a magnetic insulator. We show how the continuous system can be simulated on a 2D square lattice, without running into the fermion-doubling obstruction. For that purpose we adapt the existing tangent fermion discretization on an unbounded lattice to account for a lattice termination that simulates the magnetic insulator interface.