Electric Multipoles of Double Majorana Kramers Pairs

TL;DR

This paper proposes using electric multipole responses, free from the Meissner effect, as a novel surface-sensitive method to determine bulk Cooper-pair symmetry in topological crystalline superconductors with double Majorana Kramers pairs.

Contribution

It introduces electric response as an alternative to magnetic methods for probing Cooper-pair symmetry and explores the relationship between electric multipoles, strain, and superconducting symmetries.

Findings

Electric multipoles can reveal Cooper-pair symmetry without magnetic fields.

A specific strain irreducible representation induces a gap in double Majorana Kramers pairs.

Electric detection is viable for identifying superconducting pairing symmetries.

Abstract

A single Majorana Kramers pair hosts only one component of the magnetic multipole. This can be used to determine the bulk Cooper-pair symmetry through surface-sensitive spectroscopic measurements, either by applying a magnetic field or by using a ferromagnet/superconductor junction. This paper proposes that the electric response, which is free from the Meissner effect, can be used an alternative method to measure the bulk Cooper-pair symmetry in time-reversal-invariant superconductors with double Majorana Kramers pairs. The relationships among electric multipoles, strain tensors and superconducting symmetries under a given wallpaper group on the surfaces of topological crystalline superconductors are shown. This study also reveals that only a specific irreducible representation of a uniform strain yields a gap in the double Majorana Kramers pairs for the topological-crystalline-superconductor candidate Sr$_3$SnO. This highlights the viability of electric detection regarding Cooper-pair symmetry.