Fluxoid solitons in superconducting tapered tubes and bottlenecks

A thin-walled tubular superconductor develops a quantized fluxoid in the presence of an axial magnetic field. The fluxoid corresponds to the number of phase windings of the superconducting order parameter and is topological in nature. When the tube has a radius variation along the axial direction, forming a bottleneck structure between sections with different radius, a fluxoid mismatch can appear depending on the applied magnetic field. The bottleneck then becomes a topological boundary and is host to topologically protected solutions for the order parameter, dubbed fluxoid solitons, that are free to move around bottlenecks with cylindrical symmetry. Fluxoid solitons are a new type of vortex with non-quantized flux, loosely related to Pearl vortices in thin superconducting films and fluxons in Corbino Josephson junctions. We characterize their properties as a function of system parameters using the self-consistent quasiclassical theory of diffusive superconductors. We consider both short bottleneck structures and long tapered tubes, where multiple trapped fluxoid solitons adopt elaborate arrangements dictated by their mutual repulsion.