Classification of Weyl point trajectories in multi-terminal Josephson junctions

We theoretically study Weyl points emerging in multi-terminal Josephson junctions (MTJJ). We focus on how the trajectories of the Weyl points evolve when the gate voltage of a quantum point contact (QPC) is varied. MTJJ is a Josephson junction with three or more superconducting terminals. The spectrum of Andreev bound state of the MTJJ is 2π periodic in the superconducting phase differences φ between terminals and can be viewed as a band structure. In particular, previous studies have established that four-terminal systems host topologically protected Weyl points in the three-dimensional phase-difference space. We show that the Weyl points can be steered by the QPC gate and that their trajectories fall into three differnet classes. These trajectories are characterized by the topological invariant, the Chern number. Furthermore, in five-terminal systems we obtain more intricate trajectories together with a rich topological phase diagram.