Clusters of vortices induced by thermal gradient in mesoscopic superconductors

The structural and magnetic properties of the vortex matter in mesoscopic superconductors have been of great interest in the last decades. Recently, it has been found that vortex-vortex interaction, which is generally repulsive, can be non-monotonic under some special circumstances. Here, we have studied this issue by applying the three dimensional time dependent Ginzburg-Landau equations to a thin type-I mesoscopic superconducting film under a thermal gradient. We find that this favors the formation of small clusters of vortices in some special domains of the superconductor. We also find that this is intimately related to the non-monotonic vortex-vortex interaction by investigating the behavior of two constrained vortices in the presence of a thermal gradient. We show that the vortex-vortex interaction alternates between short range attraction and long range repulsion. This study shows that the thermal gradient has the potential to be an important tool to manipulate the vortex matter.