Spontaneous generation of vortices by a nonuniform Zeeman field in a two-dimensional Rashba-coupled superconductor

The interplay of the electron exchange interaction and spin-orbit coupling results in spontaneous supercurrents near magnetic insulator islands, which are placed on the top of a two-dimensional (2D) superconductor, and whose magnetization is parallel to 2D electron gas. It is shown that in contrast to the well-studied situation, where such an effect involves only topologically trivial spatial variations of the superconducting order parameter, one should take into account supercurrent vortices. The latter are spontaneously generated around the island's boundary of an arbitrary shape, and they result in screening of the Zeeman field. This problem has been considered for electrons subject to a strong Rashba spin-orbit coupling, including Dirac systems as well. In the latter case, vortices can carry Majorana zero modes.