Domain walls and non-integral flux penetration in superconductors having broken time-reversal symmetry

$\textrm{Sr}_2\textrm{RuO}_4$ is a candidate material for realizing superconductivity that spontaneously breaks time-reversal symmetry~[1]. If this symmetry is in fact broken then the spatial pattern of the superconductivity may break up into domains that differ in their chirality, separated by domain walls. A consistent picture of how, where, or whether such domain walls form in $\textrm{Sr}_2\textrm{RuO}_4$ has, however, yet to emerge~[2]. It has been predicted that, owing to in-plane crystalline anisotropy, a domain wall may catalyze the dissociation of a unit-flux vortex (measured in units of the superconducting flux quantum $\Phi_0$) into two fractional-flux vortices, the fluxes of which sum to unity~[3]. In the present work, we consider a domain wall in which there is a relatively sharp bend through an angle $\Theta$. We show that, even in the absence of crystalline anisotropy, such a wall is penetrated by a magnetic field localized to the vicinity of the bend, of total, non-quantized flux $\Phi_{0}\Theta/\pi$. (Anisotropy, weak in $\textrm{Sr}_2\textrm{RuO}_4$, gives a small correction to this result.)\thinspace\ The observation of localized regions carrying non-integer flux would provide evidence for domain walls separating chiral domains of superconductivity. \par\noindent [1]~A.\ P.\ Mackenzie and Y.\ Maeno, Rev.\ Mod.\ Phys.\ {\bf 75\/}, 657 (2003). \hfil\break\noindent [2]~C.\ Kallin and A.\ J.\ Berslinsky, arXiv:0902.2170v1 (2009). \hfil\break\noindent [3]~M.\ Sigrist and D.] F.\ Agterberg, Prog.\ Theor.\ Phys {\bf 102\/}, 965 (1999).