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

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.