Majorana multipole response with magnetic point group symmetry

TL;DR

This paper extends the concept of Majorana multipole responses to magnetic point group symmetries, classifying possible electromagnetic responses of Majorana fermions and linking them to superconducting pairing symmetries, especially in time-reversal-breaking systems.

Contribution

It provides a topological classification of Majorana fermion responses under magnetic symmetries and predicts higher-order multipole responses like quadrupoles in time-reversal-breaking superconductors.

Findings

Classified Majorana multipole responses for magnetic symmetries.

Identified magnetic quadrupole responses in specific superconductors.

Linked responses to underlying Cooper pair symmetries.

Abstract

Majorana fermions (MFs) in a topological superconductor exhibit anisotropic electromagnetic responses, called Majorana multipole responses, when MFs are degenerate under time-reversal and crystalline symmetries. In time-reversal symmetric systems, the Majorana multipole response relates to Cooper pair symmetry in the underlying superconducting material, which provides a way to identify pairing symmetries through surface-spin-sensitive measurements. Here, we extend the concept of Majorana multipole response to systems with magnetic point group symmetry that break time-reversal symmetry and clarify how the response of MFs includes information about underlying superconductors. From a topological classification of symmetry-protected MFs and an effective surface theory, we classify possible magnetic and electric responses for MFs, which manifests a direct connection to Cooper pair symmetry for a symmetry-enforced pair of MFs. Additionally, we find several time-reversal-even higher-order multipole responses, such as the quadrupole response, which are forbidden in time-reversal symmetric systems, whereby indicating breaking of time-reversal symmetry. The theory is applied to the odd-parity chiral superconductor UTe$_2$ and the ferromagnetic superconductor UCoGe, demonstrating the appearance of a magnetic quadrupole response on a surface.