Time-reversal anomaly and Josephson effect in time-reversal invariant topological superconductors

TL;DR

This paper explores the unique Josephson effects caused by time-reversal anomaly in topological superconductors, proposing experimental signatures to identify their topological nature.

Contribution

It introduces the concept of time-reversal anomaly in topological superconductors and predicts distinctive Josephson effects as experimental signatures.

Findings

Half-period Josephson current-flux relation in SQUIDs

Restoration of normal Josephson coupling with in-plane magnetic field

Proposal for experimental verification of topological superconductivity

Abstract

Topological superconductors are gapped superconductors with protected Majorana surface/edge states on the boundary. In this paper, we study the Josephson coupling between time-reversal invariant topological superconductors and s-wave superconductors. The Majorana edge/surface states of time-reversal invariant topological superconductors in all physical dimensions 1, 2, 3 have a generic topological property which we named as time-reversal anomaly. Due to the time-reversal anomaly, the Josephson coupling prefers a nonzero phase difference between topological and trivial superconductors. The nontrivial Josesphon coupling leads to a current-flux relation with a half period in a SQUID geometry, and also a half period Fraunhofer effect in dimension higher than one. We also show that an in-plane magnetic field restores the ordinary Josephson coupling, as a sharp signature that the proposed effect is a consequence of the unique time-reversal property of the topological edge/surface states. Our proposal provides a general approach to experimentally verify whether a superconductor is topological or not.