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Majorana multipole response of topological superconductors

Shingo Kobayashi

In contrast to elementary Majorana particles, emergent Majorana fermions (MFs) in condensed-matter systems may have electromagnetic multipoles. We develop a general theory of magnetic multipoles for surface helical MFs on time-reversal-invariant superconductors. The results show that the multipole response is governed by crystal symmetry, and that a one-to-one correspondence exists between the symmetry of Cooper pairs and the representation of magnetic multipoles under crystal symmetry [1,2]. The latter property provides a way to identify unconventional pairing symmetry via the magnetic response of surface MFs. Furthermore, we find new magnetic responses: one is a magnetic-octupole response on superconductors with spin-3/2 electron, which uniquely characterizes high-spin superconductors [2]. The other is a magnetic-quadrupole response on superconductors with nonsymmorphic symmetry [3].



[1] Y. Xiong, A. Yamakage, S. Kobayashi, M. Sato, and Y. Tanaka, Crystals 7, 58 (2017).

[2] S. Kobayashi, A. Yamakage, Y. Tanaka, and M. Sato, Phys. Rev. Lett. 123, 097002 (2019)

[3] Y. Yamazaki, S. Kobayashi, and A. Yamazaki, arXiv: 1912.07939