Josephson effect in type-I Weyl semimetals

Abstract

The emergent Weyl fermions in condensed matter generally break the Lorentz invariance, resulting in a tilted (type-I) or overtilted (type-II) energy dispersion. The tilting energy spectra can lead to exotic quantum interference effects in a junction setup. Here, we theoretically investigate the Josephson current in a Weyl superconductor–Weyl (semi)metal–Weyl superconductor junction of a time-reversal (TR) broken type-I Weyl semimetal. We reveal a Josephson current 0-π transition and zero-bias supercurrent for BCS-like pairing with inversion-symmetric tilt in the Weyl nodes. The zero-bias current is the manifestation of the tilt-assisted anomaly in this model. In contrast, these anomalous effects remain absent in the case of inversion-breaking tilt and for Fulde-Ferrell-Larkin-Ovchinnikov-like pairing in the Weyl superconductor. We further chart qualitative differences between the two distinct types of pairings by studying the critical current dependency on junction length. Our study opens an avenue to probe these two types superconducting pairings in TR-broken Weyl semimetals. It is also quite interesting that the tilting in Weyl nodes naturally leads to anomalous current phase relations in this model without any magnetic manipulation.

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