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.
Highlights
Superconducting states that spontaneously break timereversal symmetry (BTRS) have been a subject of experimental pursuit and theoretical investigation over the past few decades
We study the spontaneous magnetic field generated by pinned domain walls as a function of their orientation with respect to the crystalline axes
Superconducting states with spontaneously broken timereversal symmetry are of great current interest, identifying the type of BTRS order parameter is a notoriously difficult problem
Summary
Superconducting states that spontaneously break timereversal symmetry (BTRS) have been a subject of experimental pursuit and theoretical investigation over the past few decades. Spontaneous magnetic fields appear in an isotropic system if one creates cross-gradients of relative density and relative phase [9] Such configurations arise when domain walls interact with pinning centers or the boundary of the sample [9]. We focus on a simple feature to measure and compare, showing how the states can be diagnosed via the observation of the magnetic field of domain walls separating s + is and s − is or s + id and s − id domains This can be observed in scanning superconducting quantum interference device (SQUID), scanning Hall probes [22,23,24,25], and muon spin rotation [2]. It is proposed that this behavior can be studied experimentally to determine the pairing symmetry of the superconducting state
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