  In contrast to elementary Majorana particles, emergent Majorana fermions
(MFs) in condensed-matter systems may have electromagnetic multipoles. We
developed 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. The latter property provides a way to
identify nonconventional pairing symmetry via the magnetic response of surface
MFs. We also find that most helical MFs exhibit a magnetic-dipole response, but
those on superconductors with spin-3/2 electrons may display a
magnetic-octupole response in leading order, which uniquely characterizes
high-spin superconductors. Detection of such an octupole response provides
direct evidence of high-spin superconductivity, such as in half-Heusler
superconductors.

Superconductivity;Mesoscale and Nanoscale Physics;Strongly Correlated Electrons