Helical Andreev bound states and superconducting Klein tunneling in topological insulator Josephson junctions

Currently, much effort is being put into detecting unconventional p-wave superconductivity in Josephson junctions based on topological insulators (TIs). For that purpose we propose to use superconducting Klein tunneling, i.e., the reflectionless passage of Cooper pairs through a potential barrier in a gated ballistic junction. This phenomenon occurs due to the fact that the supercurrent is carried by helical Andreev bound states (ABSs) characterized by spin-momentum locking similar to the normal-state carriers. We derive the spectrum of the helical ABSs and the corresponding Josephson current for a junction made on the surface of a three-dimensional TI. The superconducting Klein tunneling is predicted to yield a nonsinusoidal current-phase relation and an anomalous critical current Ic that does not vanish with increasing barrier strength. We also analyze the dependence of the IcRₙ product (where Rₙ is the normal-state junction resistance) on the microscopic parameters of the superconductor/TI interface, which leads to lower IcRₙ values than expected from previous models of the proximity-effect Josephson junctions.