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

TL;DR

This paper presents a novel lattice implementation of massless Dirac fermions that preserves a topologically protected Dirac cone, avoiding common discretization issues like fermion doubling and zone boundary singularities.

Contribution

The authors introduce a space-time lattice model for Dirac fermions that maintains topological protection of the Dirac cone, unlike traditional discretizations.

Findings

The model exhibits a tangent dispersion with a single Dirac cone.

Topological protection requires breaking both time-reversal and chiral symmetries to gap the cone.

Standard linear sawtooth discretization lacks this protection due to discontinuities at zone boundaries.

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.