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

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 Ba 1−x K x Fe 2 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 fields 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.

Magnetic field behavior in s+is and s+id superconductors: Twisting of applied and spontaneous fields

“…Hence, excitations that are commonly associated with purely the matter fields, such as domain walls and defects, in s+is and s+id models will exhibit a spontaneous magnetic response. This confirms previous numerical calculations that have been performed for domain walls 34 . It has been suggested that defects do not produce spontaneous magnetic field in such models 38 .…”

“…The twisting angle is given in Eq. 35 and determines the amount the local magnetic field twists away from the external field direction. We have also plotted the normalised energy density F = F − F 0 , the condensate densities ρ 1 ,ρ 2 and phase difference θ 12 = θ 1 − θ 2 .…”

“…In an isotropic two-component BTRS model this forms a 2dimensional wall in the condensates only, with normal parallel to x 1 . However, it has recently been shown that in s + is and s + id models, domain walls also exhibit spontaneous magnetic field 34 . The linearization in section III offers a way of both explaining and predicting the form of these spontaneous fields.…”

“…In contrast to the better studied p + ip systems, the spontaneous fields generated in s + is superconductors have only recently started to be explored 19,27,28,[40][41][42] . In particular in 34 a comparative study was presented of the magnetic fields generated by domain walls in both s + is and s + id superconductors.…”

“…Both s + is and s + id systems are characterized not only by spontaneous breakdown of time reversal symmetry (BTRS) but also by the appearance of non-collinear gradients of the inter-component phase difference and relative densities around impurities [1,[33][34][35].…”