Josephson Effects of the Monopole Superconductor*

As an exotic type of three-dimensional topological superconductors, monopole superconductors arise from the non-trivial Berry phase of Cooper pairs. Its unconventional pairing symmetry is characterized by monopole harmonic functions and can be potentially realized in doped magnetic Weyl semimetals. To have clear understanding of its pairing properties, the phase sensitive transport measurement is crucial. We study the Josephson effects between monopole superconductors and between a monopole superconductor and an s-wave superconductor. For a Josephson junction coupling two identical monopole superconductors, we find that its behavior is similar with that in a junction coupling two identical chiral p-wave superconductors. In sharp contrast, the Josephson junction that couples two monopole superconductors related by time reversal symmetry exhibits an additional π-shift contribution from a part of its Fermi surfaces in its current phase relation. For a Josephson junction coupling a monopole superconductor and an s-wave superconductor, its current phase relation exhibits 2π-periodicity, which is apparently different from that with π-periodicity for the junction between chiral p-wave and s-wave superconductors. Combining the results above, it provides a distinguishing feature to identify monopole superconductors in experiments.

This work was supported as part of the Institute for Quantum Matter, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award No. DE-SC0019331.