Josephson signatures of Weyl node creation and annihilation in irradiated Dirac semimetals

Weyl node creation and annihilation are unique topological phenomena associated with Weyl fermions. Besides the magnetic field, high-frequency illumination can also break the time-reversal symmetry and induce the creation and annihilation of Weyl nodes from a Dirac semimetal. Experimentally, the Weyl node creation and annihilation induced by a magnetic field have been verified by the signature of negative magnetoresistance. In this work, instead of magnetoresistance signatures by application of a magnetic field, we theoretically study the Josephson signatures of Weyl node creation and annihilation in irradiated Dirac semimetals. It is found that Weyl node creation is accompanied by a two-mode oscillation and 0-$\ensuremath{\pi}$ transitions in the Josephson current. We further illustrate that two oscillation modes stem from two Andreev reflection processes: opposite-chirality and equal-chirality Andreev reflections, respectively. With Weyl node annihilation, the Josephson current is first shut down and then recovered by the activation of spin-flipping at interfaces by two ferromagnets. The recovered anomalous Josephson current has an arbitrary and tunable ground-state phase difference, other than 0 and $\ensuremath{\pi}$. These predictions are helpful for experimental observation of illumination-induced Weyl node creation and annihilation.