Massless Dirac Fermions on a Space‐Time Lattice with a Topologically Protected Dirac Cone

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 an implementation of Dirac fermions on a space‐time lattice that removes both obstructions is introduced. 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. It is shown 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. Fermion doubling is a lattice artefact that appears if one discretizes the Dirac equation of massless electrons. One can work around this obstacle by replacing the linear dispersion by a sawtooth. Here it is shown that this method opens a gap at the Dirac point of the band structure. A replacement of the sawtooth by a tangent cures that deficiency.