Majorana multipole response: General theory and application to wallpaper groups

TL;DR

This paper develops a theoretical framework linking Majorana fermion electromagnetic responses to Cooper pair symmetry, enabling identification of unconventional superconducting states through surface measurements and external fields.

Contribution

It introduces a multipole theory of Majorana fermions in topological superconductors, establishing a direct correspondence with Cooper pair symmetry and predicting novel magnetic responses.

Findings

Majorana fermions exhibit electromagnetic responses reflecting Cooper pair symmetry.

High-spin or nonsymmorphic superconductors may show magnetic octupole responses.

Electric responses of Majorana Kramers pairs are characterized.

Abstract

Whereas identification of Cooper pair symmetry is the first and crucial step in the investigation of unconventional superconductors, only a few have been established so far because of its own difficulties. To solve this problem, we develop a theory for identification of pairing symmetry using knowledge of topological superconductivity. Establishing the multipole theory of emergent Majorana fermions in time-reversal-invariant topological superconductors, we discover a one-to-one correspondence between the electromagnetic response of Majorana fermions and Cooper pair symmetry. The emergent Majorana fermions host magnetic structures that share the same irreducible representation with Cooper pairs under crystalline symmetry. We furthermore reveal that Majorana fermions in high-spin or nonsymmorphic superconductors may exhibit magnetic octupole responses, which give a direct evidence of these exotic superconducting states. Electric responses of multiple Majorana Kramers pairs are also clarified. Our theory provides the fundamentals for identification of unconventional Cooper pairings through surface-spin-sensitive measurements as well as that for manipulation of Majorana fermions by external electromagnetic fields.