Trapping magnetic flux quanta in superconducting 3D caps

Abstract

Magnetic flux quanta in type-II superconductors are topological excitations of the order parameter whose sensitivity to the local environment makes them probes of current density, magnetic fields, and pinning landscapes. Yet, in planar thin films, individual vortices are difficult to manipulate, often requiring intricate nanopatterning or demanding scanning-probe instrumentation. Here, we show that shaping a superconducting thin film into a three-dimensional curved geometry enables controllable vortex trapping under a spatially uniform applied magnetic field. Employing a conformal formulation of the time-dependent Ginzburg-Landau equation, we simulate vortex dynamics in a cap-shaped superconducting membrane and compare it with a planar reference. Curvature converts the uniform applied magnetic field into a nonuniform local normal component, creating a reconfigurable asymmetric rim-pinning potential tunable by magnetic-field orientation. Rotating the magnetic field therefore controls the number and positions of vortices trapped along the rim. Moreover, the asymmetric pinning produces a superconducting diode effect through current-direction-dependent vortex capture. Three-dimensional curvature thus provides a route to engineer local vortex pinning and realize fluxonic devices with magnetic-field-programmable vortex trapping and transport.