Vortex-antivortex phenomena in superconductors with antidot arrays

We investigated in detail the vortex configurations in superconducting films with regular antidot-arrays within the non-linear Ginzburg-Landau theory, where demagnetization effects and overlapping vortex cores are fully taken into account (contrary to the London approach). In addition to the well-known matching phenomena, we predict: (i) the \textit{nucleation of giant-vortex states} at interstitial sites; (ii) the \textit{combination of giant- and multi-vortices} at rational matching fields; and (iii) for particular interstitial vorticity, the symmetry imposed creation of \textit{vortex-antivortex configurations}. As a consequence of (iii), we predict \textit{resistance maxima }at particular matching fields, opposite to the expected minima due to commensurability effects. Using the same principle, we stabilized vortex-antivortex molecules in finite submicron superconducting polygons by strategically placed nanoholes. Compared to earlier predictions, we \textit{enhanced} the stamina of the antivortex with respect to temperature, applied fields and geometrical defects in the sample. Further, increased vortex-antivortex spacing and pronounced amplitudes of the local magnetic field in our system make these fascinating structures \textit{observable} by e.g. Scanning Tunneling or Hall probe microscopy.