Penetration of nonquantized magnetic flux through a domain-wall bend in time-reversal symmetry broken superconductors

TL;DR

This paper predicts that in time-reversal symmetry-breaking superconductors, domain walls with bends can host nonquantized magnetic flux, providing a potential experimental signature of such unconventional superconductivity.

Contribution

It introduces a phenomenological model linking domain wall bends to nonquantized magnetic flux in chiral superconductors, offering a new way to detect time-reversal symmetry breaking.

Findings

A bent domain wall hosts a nonquantized magnetic flux proportional to the bend angle.

Localized nonquantized flux can indicate the presence of domain walls between chiral domains.

The model applies to Sr$_2$RuO$_4$ and similar unconventional superconductors.

Abstract

It has been proposed that the superconductivity of Sr$_2$RuO$_4$ is characterized by pairing that is unconventional and, furthermore, spontaneously breaks time-reversal symmetry. However, one of the key expected consequences, viz., that the ground state should exhibit chiral charge currents localized near the boundaries of the sample, has not been observed, to date. We explore an alternative implication of time-reversal symmetry breaking: the existence of walls between domains of opposing chirality. Via a general phenomenological approach, we derive an effective description of the superconductivity in terms of the relevant topological variables (i.e., domain walls and vortices). Hence, by specializing to the in the in-plane rotationally invariant limit, we show that a domain wall that is translationally invariant along the z axis and includes a bend through an angle $\Theta$ is accompanied by a nonintegral (and possibly nonquantized) magnetic {\it bend flux} of $\big((\Theta/\pi)+n\big)\Phi_0$, with integral $n$, that penetrates the superconductor, localized near the bend. We generalize this result to the situation in which gauge transformations and rotations about the z axis are degenerate transformations of the chiral superconducting order. On the basis of the specialized result and its generalization, we note that any observation of localized, nonquantized flux penetrating a z-axis surface (e.g., via scanned-probe magnetic imaging) can be interpreted in terms of the presence of bent walls between domains of opposing chirality, and hence is suggestive of the existence of time-reversal symmetry-breaking superconductivity.