Squeezed and nascent vortices in a thin normal layer with proximity induced superconductivity

It is theoretically found that in-plane vortices may exist in a thin normal metal (N) layer (with thickness dN much smaller than the coherence length ξN) that covers a superconductor (S). Vortices enter the N layer with proximity-induced superconductivity at a sufficiently large in-plane magnetic field. These vorticies have squeezed cores and are located (pinned) near the SN interface. At large magnetic fields, we find a nascent vortex state, which is a spatially modulated state along the finite length N layer with zero vorticity. This state does not exist in a finite length single S layer.