Generalized eigenproblem without fermion doubling for Dirac fermions on a lattice
M. J. Pacholski, G. Lemut, J. Tworzydło, C. W. J. Beenakker
SciPost Phys. 11, 105 (2021) · published 14 December 2021
- doi: 10.21468/SciPostPhys.11.6.105
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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.
Cited by 9
Authors / Affiliations: mappings to Contributors and Organizations
See all Organizations.- 1 Michał Pacholski,
- 1 Gal Lemut,
- 2 Jakub Tworzydlo,
- 1 Carlo Beenakker
- Horizon 2020 (through Organization: European Commission [EC])
- Nederlandse Organisatie voor Wetenschappelijk Onderzoek / Netherlands Organisation for Scientific Research [NWO]