Direct imaging of vortex polygons and vortex shells in mesoscopic squares of a weak pinning superconducting thin film

We report on the direct visualization of vortices in mesoscopic squares of a weak pinning amorphous superconducting thin film using a scanning superconducting quantum interference device microscope. From systematic measurements made on selected dots, we trace how the vortex pattern evolves with an applied magnetic fi eld. The observed images clearly illustrate the formation of symmetric polygons and concentric shells of vortices, from which the rule of shell filling with increasing vorticity is formulated. We analyze the size and shape of vortex polygons and obtain insight into the flow pattern of the shielding current governing vortex configurations.