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The effect of spatial inhomogeneity on the properties of a two-dimensionalnon-centrosymmetric superconductor in an in-plane magnetic field isinvestigated, as it can be realized in LaAlO_3-SrTiO_3 interfaces. Wedemonstrate that the spatial variation of Rashba spin-orbit coupling (RSOC)yields a local magnetic flux pattern due to the field-induced inhomogeneoushelical phase. For sufficiently strong fields, vortices can nucleate atinhomogeneities of the RSOC.

Model for magnetic flux pattern induced by in-plane magnetic fields on spatially inhomogeneous superconducting interfaces of LaAlO_3-SrTiO_3