Finite-difference method for transport of two-dimensional massless Dirac fermions in a ribbon geometry

TL;DR

This paper introduces a numerical finite-difference method to compute the conductance of 2D massless Dirac fermions in disordered systems, effectively handling boundary conditions, magnetic fields, and long-range disorder without fermion doubling.

Contribution

The paper presents a novel discretization scheme that avoids fermion doubling and is suitable for long-range disorder in Dirac materials, extending computational capabilities.

Findings

Method successfully computes conductance in disordered graphene ribbons.

Boundary conditions and magnetic fields are incorporated effectively.

Long-range disorder effects are analyzed using the new scheme.

Abstract

We present a numerical method to compute the Landauer conductance of noninteracting two-dimensional massless Dirac fermions in disordered systems. The method allows for the introduction of boundary conditions at the ribbon edges and accounts for an external magnetic field. By construction, the proposed discretization scheme avoids the fermion doubling problem. The method does not rely on an atomistic basis and is particularly useful to deal with long-range disorder, the correlation length of which largely exceeds the underlying material crystal lattice spacing. As an application, we study the case of monolayer graphene sheets with zigzag edges subjected to long-range disorder, which can be modeled by a single-cone Dirac equation.