Nucleation of superconductivity in clean superconductor-ferromagnet hybrid structures with Rashba spin-orbit interaction

Abstract

We study the influence of the inverse proximity effect on the nucleation of superconductivity in planar hybrid structures consisting of a thin superconducting film proximity coupled to a material with a strong exchange or Zeeman field and the Rashba spin-orbit interaction. Based on numerical simulations and analytical estimates within the framework of the Gor'kov equations, we find the superconducting transition temperature of the system and determine the spatial structure of the gap function. It is shown that the spin-orbit interaction partially compensates the pair-breaking effect of the exchange or Zeeman field and stabilizes modulated superconducting states, which can be traced to the Lifshitz invariant in the Ginzburg-Landau free-energy density. The suggested approach provides a microscopic justification of this invariant for a large class of superconducting hybrid systems and clarifies the validity range of the corresponding phenomenological models with terms linear in the spatial gradients of the superconducting order parameter.