Single-cone Dirac edge states on a lattice

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.