Majorana multipole response of topological superconductors

Crystalline symmetry enriches topological phases of matter. For instance, Dirac semimetals with crystalline symmetry are one of the promising ways to realize a variety of topological superconductivity. In contrast to elementary Majorana particles, emergent Majorana fermions (MFs) in topological crystalline supercondutors 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.