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Massless Dirac fermions in an electric field propagate along the field lineswithout backscattering, due to the combination of spin-momentum locking andspin conservation. This phenomenon, known as "Klein tunneling", may be lost ifthe Dirac equation is discretized in space and time, because of scatteringbetween multiple Dirac cones in the Brillouin zone. To avoid this, a staggeredspace-time lattice discretization has been developed in the literature, withone single Dirac cone in the Brillouin zone of the original square lattice.Here we show that the staggering doubles the size of the Brillouin zone, whichactually contains two Dirac cones. We find that this fermion doubling causes aspurious breakdown of Klein tunneling, which can be avoided by an alternativesingle-cone discretization scheme based on a split-operator approach.

Reflectionless Klein tunneling of Dirac fermions: Comparison of split-operator and staggered-lattice discretization of the Dirac equation