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

It has been proposed that the superconductivity of Sr₂RuO 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-plane rotationally invariant limit, we show that a domain wall that is translationally invariant along the z axis and includes an isolated bend through an angle Θ is accompanied by a nonintegral magnetic bend flux of [(Θ/π)+n] Φ₀, 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. These results are independent of the magnitude of chiral-charge currents that are predicted to flow along the core of domain walls. On the basis of the specialized result and its generalization, we note that any observation of localized, nonintegral flux penetrating a z-axis surface (e.g., via scanned-probe magnetic imaging) could potentially 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.