Josephson current signatures of the Majorana flat bands on the surface of time-reversal-invariant Weyl and Dirac semimetals

TL;DR

This paper predicts that Majorana flat bands on the surface of time-reversal-invariant Weyl and Dirac semimetals cause a distinctive jump in Josephson current at a phase difference of π, serving as an experimental signature.

Contribution

It demonstrates that Majorana flat bands induce a measurable Josephson current jump, with specific scaling and orientation dependence, robust against temperature and disorder.

Findings

Josephson current exhibits a discontinuous jump at π phase difference.

Jump magnitude scales with junction width and Weyl node separation.

Jump remains robust under temperature and weak disorder.

Abstract

A linear Josephson junction mediated by the surface states of a time-reversal-invariant Weyl or Dirac semimetal localizes Majorana flat bands protected by the time-reversal symmetry. We show that as a result, the Josephson current exhibits a discontinuous jump at $\pi$ phase difference which can serve as an experimental signature of the Majorana bands. The magnitude of the jump scales proportionally to the junction width and the momentum space distance between the Weyl nodes. It also exhibits a characteristic dependence on the junction orientation. We demonstrate that the jump is robust against the effects of non-zero temperature and weak non-magnetic disorder.