Supercurrent and phase signatures of topological superconductivity in planar Josephson junctions

Abstract

We consider planar Josephson junctions, with dimensions as used in recent experiments, and show using numerical calculations that the junctions undergo topological superconducting transition, revealed by the appearance of zero-energy Majorana bound states at the ends of the non-superconducting channel of the junctions in the presence of an in-plane magnetic field and $\pi$ phase difference between the superconducting leads. Our main finding is that, under realistic parameter settings, the critical supercurrent undergoes a minimum and the ground state phase increases from zero toward $\pi$ at a critical field, without the junctions necessarily transitioning into a topological superconducting phase. Remarkably, the critical supercurrent minimum and a simultaneous sharp jump in the ground state phase appear in junctions that are undoubtedly in trivial superconducting phase. Our results provide updated insights for experimental detection of topological superconductivity in planar Josephson junctions using the supercurrent and phase signatures.Comment: Comments are welcom