Multipole theory of Majorana fermions in topological superconductors

The emergence of Majorana fermions is a salient feature of topological superconductors. Whereas the emergent Majorana fermions are often discussed as possible qubits of topological quantum computers, they also provide important information to identify paring symmetry of underlying unconventional superconductors. We develop here a theory of electric and magnetic responses of Majorana fermions in superconductors and clarify the relation between the electromagnetic responses and Cooper pair symmetry [1,2]. We point out that Majorana fermions belong to short representations of particle-hole or chiral symmetries, which is a group theoretical manifestation of their self-antiparticle nature. We reveal magnetic octupole responses of Majorana fermions that characterize spin 3/2 superconductors or non-symmorphic superconductors. We also apply our theory to spin 3/2 half-Heusler superconductors and other unconventional superconductors.
[1] S. Kobayashi, A. Yamakage, Y. Tanaka, M. Sato, Phys. Rev. Lett. 123, 097002 (2019).
[2] S. Kobayashi, Y. Yamazaki, A. Yamakage, M. Sato, in preparation.