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

Massless Dirac fermions in an electric field propagate along the field lines without backscattering, due to the combination of spin-momentum locking and spin conservation. This phenomenon, known as 'Klein tunneling', may be lost if the Dirac equation is discretized in space and time, because of scattering between multiple Dirac cones in the Brillouin zone. To avoid this, a staggered space-time lattice discretization has been developed in the literature, withonesingle Dirac cone in the Brillouin zone of the original square lattice. Here we show that the staggering doubles the size of the Brillouin zone, which actually containstwoDirac cones. We find that this fermion doubling causes a spurious breakdown of Klein tunneling, which can be avoided by an alternative single-cone discretization scheme based on a split-operator approach.

Deconfinement of Majorana Vortex Modes Produces a Superconducting Landau Level.

A spatially oscillating pair potential Δ(r)=Δ_{0}e^{2iK·r} with momentum K>Δ_{0}/ℏv drives a deconfinement transition of the Majorana bound states in the vortex cores of a Fu-Kane heterostructure (a 3D topological insulator with Fermi velocity v, on a superconducting substrate with gap Δ_{0}, in a perpendicular magnetic field). In the deconfined phase at zero chemical potential the Majorana fermions form a dispersionless Landau level, protected by chiral symmetry against broadening due to vortex scattering. The coherent superposition of electrons and holes in the Majorana Landau level is detectable as a local density of states oscillation with wave vector sqrt[K^{2}-(Δ_{0}/ℏv)^{2}]. The striped pattern also provides a means to measure the chirality of the Majorana fermions.

Topologically Protected Landau Level in the Vortex Lattice of a Weyl Superconductor.

The question whether the mixed phase of a gapless superconductor can support a Landau level is a celebrated problem in the context of d-wave superconductivity, with a negative answer: the scattering of the subgap excitations (massless Dirac fermions) by the vortex lattice obscures the Landau level quantization. Here we show that the same question has a positive answer for a Weyl superconductor: the chirality of the Weyl fermions protects the zeroth Landau level by means of a topological index theorem. As a result, the heat conductance parallel to the magnetic field has the universal value G=1/2g_{0}Φ/Φ_{0}, with Φ as the magnetic flux through the system, Φ_{0} as the superconducting flux quantum, and g_{0} as the thermal conductance quantum.