Magnetoelectric coupling in superconductor-helimagnet heterostructures

The Ginzburg-Landau free energy of a conventional superconductor coupled to a helimagnet is microscopically derived using functional field integral techniques. We show that the spin texture leads to a Lifshitz invariant in the free energy, which couples the momentum density of the superconducting condensate to the magnetization of the helimagnet. For helimagnets with a conical texture, the Lifshitz invariant yields a spatial modulation of the superconducting phase along the helical wave vector of the magnetic texture. Based on self-consistent numerical calculations, we verify the theoretical formalism by investigating a superconductor that contains a helical Yu-Shiba-Rusinov (YSR) chain. We demonstrate that the texture-induced magnetoelectric coupling produces a strong supercurrent along the YSR chain, which induces a detectable magnetic field.