Vortex refraction and enhanced vortex velocities at tilted superconductor-normal metal interfaces

We derive a refraction law for superconducting vortices at superconductor/normal metal (S/N) interfaces that are exposed to tilted magnetic fields. Simulations of the proximity effect confirm this law and reveal vortex trapping for low effective mass. Under transport currents, we find tilt-angle-dependent core displacements due to vortex viscosities differing across the S/N interface and characteristic voltage oscillations due to the modified vortex dynamics. Our results are important for emerging three-dimensional superconductor nanotechnologies. They offer design principles for high-current S/N devices and their interface orientation in an applied field.