Magnetic signatures of domain walls in $s+is$ and $s+id$ superconductors: observability and what that can tell us about the superconducting order parameter

TL;DR

This paper investigates magnetic signatures of domain walls in $s+is$ and $s+id$ superconductors with broken time-reversal symmetry, proposing methods to distinguish their pairing symmetries through magnetic responses.

Contribution

It provides solutions for domain walls in $s+is$ and $s+id$ superconductors, including lattice effects, and identifies qualitative differences in magnetic signatures to determine pairing symmetry.

Findings

Both models show spontaneous magnetic fields along domain walls.

Magnetic signatures differ qualitatively between $s+is$ and $s+id$ states.

A procedure is proposed to identify pairing symmetry from magnetic responses.

Abstract

One of the defining features of spontaneously broken time-reversal symmetry (BTRS) is the existence of domain walls, the detection of which would be strong evidence for such systems. There is keen interest in BTRS currently, in part, due to recent muon spin rotation experiments, which have pointed towards $\textrm{Ba}_{1-x}\textrm{K}_x\textrm{Fe}_2\textrm{As}_2$ exhibiting a remarkable case of $s$-wave superconductivity with spontaneously broken time-reversal symmetry. A key question, however, is how to differentiate between the different theoretical models which describe such a state. Two particularly popular choices of model are $s+is$ and $s+id$ superconducting states. In this paper, we obtain solutions for domain walls in $s+is$ and $s+id$ systems, including the effects of lattice anisotropies. We show that, in general, both models exhibit spontaneous magnetic field, that extend along the entire length of the domain wall. We demonstrate the qualitative difference between the magnetic signatures of $s+is$ and $s+id$ domain walls and propose a procedure to extract the superconducting pairing symmetry from the magnetic-field response of domain walls.