Vortex-antivortex patterns in mesoscopic superconductors

We have studied the nucleation of superconductivity in mesoscopic structures of different shape (triangle, square and rectangle). This was made possible by using an analytical gauge transformation for the vector potential A which gives An=0 for the normal component along the boundary line of the rectangle. As a consequence the superconductor-vacuum boundary condition reduces to the Neumann boundary condition. By solving the linearized Ginzburg-Landau equation with this boundary condition we have determined the field-temperature superconducting phase boundary and the corresponding vortex patterns. The comparison of these patterns for different structures demonstrates that the critical parameters of a superconductor can be manipulated and fine-tuned through nanostructuring