Model for magnetic flux pattern induced by in-plane magnetic fields on spatially inhomogeneous superconducting interfaces of LaAlO₃-SrTiO₃

The effect of spatial inhomogeneity on the properties of a two-dimensional non-centrosymmetric superconductor in an in-plane magnetic field is investigated, as it can be realized in LaAlO_3-SrTiO_3 interfaces. We demonstrate that the spatial variation of Rashba spin-orbit coupling (RSOC) yields a local magnetic flux pattern due to the field-induced inhomogeneous helical phase. For sufficiently strong fields, vortices can nucleate at inhomogeneities of the RSOC.