# Majorana multipole response of topological superconductors

## TL;DR

This paper develops a theory linking the electromagnetic multipole responses of Majorana fermions on superconductor surfaces to crystal symmetry, enabling identification of unconventional pairing and high-spin superconductivity.

## Contribution

The authors establish a general framework connecting Majorana fermion multipole responses to crystal symmetry and pairing, revealing unique signatures of high-spin superconductors.

## Key findings

- Most helical Majorana fermions exhibit magnetic-dipole responses.
- High-spin superconductors can show magnetic-octupole responses in surface Majorana fermions.
- Magnetic response signatures can identify unconventional pairing and high-spin states.

## Abstract

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.