The effect of the Abrikosov vortex phase on spin and charge states in magnetic semiconductor-superconductor hybrids

We explore the possibility of using the inhomogeneous magnetic field carried by an Abrikosov vortex in a type-II superconductor to localize spin-polarized textures in a nearby magnetic semiconductor quantum well. We show how Zeeman-induced localization induced by a single vortex is indeed possible, and use these results to investigate the effect of a periodic vortex array on the transport properties of the magnetic semiconductor. In particular, we find an unconventional Integer Quantum Hall regime, and predict directly testable experimental consequences due to the presence of the periodic spin polarized structure induced by the superconducting vortex lattice in the magnetic semiconductor.