Superconducting films with antidot arrays - novel behavior of the critical current

Novel behavior of the critical current density $j_c$ of a regularly perforated superconducting film is found, as a function of applied magnetic field $H$. Previously pronounced peaks of $j_c$ at matching fields were always found to decrease with increasing $H$. Here we found a {\it reversal of this behavior} for particular geometrical parameters of the antidot lattice and/or temperature. This new phenomenon is due to a strong ``caging’’ of interstitial vortices between the pinned ones. We show that this vortex-vortex interaction can be further tailored by an appropriate choice of the superconducting material, described by the Ginzburg-Landau parameter $\kappa$. In effective type-I samples we predict that the peaks in $j_c(H)$ at the matching fields are transformed into a {\it step-like behavior}.