Chiral anomaly induced oscillations in the Josephson current in Weyl semimetals

Weyl semimetals are a three dimensional topological phase of matter with linearly dispersed Weyl points which appear in pairs and carry opposite chirality. The separation of paired Weyl points allows charge transfer between them in the presence of parallel electric and magnetic fields, which is known as the chiral anomaly. In this paper, we theoretically study the influence of the chiral anomaly induced chiral charge imbalance on the Josephson current in a Weyl superconductor-Weyl semimetal-Weyl superconductor junction. In Weyl superconductors, two types of pairings are considered, namely, zero momentum BCS-like pairing and finite momentum FFLO-like pairing. For BCS-like pairing, we find that the Josephson current exhibits $0$-$\pi$ transitions and oscillates as a function of $\lambda_{0} L$, where $\lambda_{0}$ is the chirality imbalance induced by the parallel electric and magnetic fields and $L$ is the length of the Weyl semimetal. The amplitude of the Josephson current also depends on the angle $\beta$ between the line connecting two paired Weyl points and the transport direction along the junction. For FFLO-like pairing, the chirality imbalance induced periodic oscillations are absent and the Josephson current is also independent of the angle $\beta$. These findings are useful in detecting the chiral anomaly and distinguishing the superconducting pairing mechanism of Weyl semimetals.