Generalized eigenproblem without fermion doubling for Dirac fermions on a lattice

Abstract

The spatial discretization of the single-cone Dirac Hamiltonian on the surface of a topological insulator or superconductor needs a special "staggered" grid, to avoid the appearance of a spurious second cone in the Brillouin zone. We adapt the Stacey discretization from lattice gauge theory to produce a generalized eigenvalue problem, of the form $\mathcal{H}\psi =E\mathcal{P}\psi$, with Hermitian tight-binding operators $\mathcal{H}$, $\mathcal{P}$, a locally conserved particle current, and preserved chiral and symplectic symmetries. This permits the study of the spectral statistics of Dirac fermions in each of the four symmetry classes A, AII, AIII, and D.

16 pages, 3 figures

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• Reflectionless Klein tunneling of Dirac fermions: Comparison of split-operator and staggered-lattice discretization of the Dirac equation
• Luttinger liquid tensor network: sine versus tangent dispersion of massless Dirac fermions
• Geometry-independent tight-binding method for massless Dirac fermions in two dimensions
• Method to preserve the chiral-symmetry protection of the zeroth Landau level on a two-dimensional lattice
• Boundary-induced Majorana coupling in a planar topological Josephson junction
• Single-cone Dirac edge states on a lattice
• Effect of Uncorrelated On-site Scalar Potential and Mass Disorder on Transport of Two-Dimensional Dirac Fermions
• Boundary-condition-assisted chiral-symmetry protection of the zeroth Landau level on a two-dimensional lattice