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

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