Massless Dirac fermions on a space-time lattice with a topologically protected Dirac cone

Abstract

The symmetries that protect massless Dirac fermions from a gap opening may become ineffective if the Dirac equation is discretized in space and time, either because of scattering between multiple Dirac cones in the Brillouin zone (fermion doubling) or because of singularities at zone boundaries. Here we introduce an implementation of Dirac fermions on a space-time lattice that removes both obstructions. The quasi-energy band structure has a tangent dispersion with a single Dirac cone that cannot be gapped without breaking both time-reversal and chiral symmetries. We show that this topological protection is absent in the familiar single-cone discretization with a linear sawtooth dispersion, as a consequence of the fact that there the time-evolution operator is discontinuous at Brillouin zone boundaries.

Accepted for publication in Annalen der Physik on 2022-09-09

References in corpus (4)

• Wave packet dynamics and valley filter in strained graphene
• Finite difference method for transport properties of massless Dirac fermions
• Generalized eigenproblem without fermion doubling for Dirac fermions on a lattice
• Reflectionless Klein tunneling of Dirac fermions: Comparison of split-operator and staggered-lattice discretization of the Dirac equation

Cited by in corpus (7)

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• Topologically protected Casimir effect for lattice fermions
• Helical Luttinger liquid on a space-time lattice
• Goos-Hänchen Shift and Photonic Spin Hall Effect in Semi-Dirac Material Heterostructures
• Luttinger liquid tensor network: sine versus tangent dispersion of massless Dirac fermions
• Reflectionless Klein tunneling of Dirac fermions: Comparison of split-operator and staggered-lattice discretization of the Dirac equation
• Method to preserve the chiral-symmetry protection of the zeroth Landau level on a two-dimensional lattice