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

TL;DR

This paper predicts that topological insulator Josephson junctions exhibit superconducting Klein tunneling due to helical Andreev bound states, resulting in unique current-phase relations and anomalous critical currents.

Contribution

It introduces the concept of superconducting Klein tunneling in topological insulator Josephson junctions and derives the spectrum of helical Andreev bound states.

Findings

Non-sinusoidal current-phase relation predicted

Critical current does not vanish with barrier strength

Lower I_c R_n values than previous models

Abstract

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 non-sinusoidal current-phase relation and an anomalous critical current $I_c$ that does not vanish with increasing barrier strength. We also analyze the dependence of the I_cR_n product (where R_n is the normal-state junction resistance) on the microscopic parameters of the superconductor/TI interface, which leads to lower I_cR_n values than expected from previous models of the proximity-effect Josephson junctions.