Vortices in a wedge made of a type-I superconductor

Using the time-dependent Ginzburg-Landau approach, we analyze vortex states and vortex dynamics in type-I superconductor films with a thickness gradient in one direction. In the thinnest part of the structures under consideration, the equilibrium states manifest the typical type-II vortex patterns with only singly-quantized vortices. At the same time, in the regions with larger thickness the singly-quantized and giant vortices coexist, in a qualitative agreement with our scanning Hall probe microscopy measurements on relatively thick Pb films. In the presence of an external current applied perpendicularly to the thickness gradient direction, the singly-quantized vortices, which enter the wedge through its thinnest edge, merge into giant vortices when propagating to the thicker parts of the structure. Remarkably, the results of our simulations imply that at moderate external current densities a regime is possible where the winding number of giant vortices, formed as a result of vortex coalescence, takes preferentially (or even exclusively) the values given by positive integer powers of two.