Generalized eigenproblem without fermion doubling for Dirac fermions on a lattice

SciPost Physics, vol. 11

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 \bm{\mathcal H}\bm{\psi}=\bm{E}\bm{\mathcal P}\bm{\psi} ℋ 𝛙 = 𝐄 𝒫 𝛙 , with Hermitian tight-binding operators \bm{\mathcal H} ℋ , \bm{\mathcal P} 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.

Authors 4

1. M. J. Pacholski Aachen Instituut-Lorentz

   Leiden University

   Affiliation as printed

   Lorentz Institute

   Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands

2. G. Lemut Aachen Instituut-Lorentz

   Leiden University

   Affiliation as printed

   Lorentz Institute

   Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands

3. J. Tworzydło

   University of Warsaw

   Affiliation as printed

   University of Warsaw

   Faculty of Physics, University of Warsaw, ul. Pasteura 5, 02-093 Warszawa, Poland

4. C. W. J. Beenakker Aachen Instituut-Lorentz

   Leiden University

   Affiliation as printed

   Lorentz Institute

   Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands