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, withsingle Dirac cone in the Brillouin zone of the original square lattice.

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}].

Complete Many-Body Localization in the t-J Model Caused by a Random Magnetic Field.

The many body localization (MBL) of spin-1/2 fermions poses a challenging problem. It is known that the disorder in the charge sector may be insufficient to cause full MBL. Here, we study dynamics of a single hole in one dimensional t-J model subject to a random magnetic field.