Supercurrent diode with high winding vortex

Nonreciprocal supercurrent refers to the phenomenon where the maximum dissipationless current in a superconductor depends on its direction of flow. This asymmetry underlies the operation of superconducting diodes and is often associated with the presence of vortices. Here, we investigate supercurrent nonreciprocal effects in a superconducting weak-link hosting distinct types of vortices. We demonstrate how the winding number of the vortex, its spatial configuration, and the shape of the superconducting lead can steer the sign and amplitude of the supercurrent rectification. We identify a general criterion for optimizing the rectification amplitude based on vortex patterns, focusing on configurations where the first harmonic of the supercurrent vanishes. We prove that supercurrent nonreciprocal effects can be used to diagnose high-winding vortex and to distinguish between different types of vorticity. Our results provide a toolkit for controlling supercurrent rectification through vortex phase textures and detecting unconventional vortex states.