Vortex configurations and critical parameters in superconducting thin films containing antidot arrays: Nonlinear Ginzburg-Landau theory

Using the non-linear Ginzburg-Landau (GL) theory, we obtain the possible vortex configurations in superconducting thin films containing a square lattice of antidots. The equilibrium structural phase diagram is constructed which gives the different ground-state vortex configurations as function of the size and periodicity of the antidots for a given effective GL parameter $\kappa^{*}$. Giant-vortex states, combination of giant- and multi-vortex states, as well as symmetry imposed vortex-antivortex states are found to be the ground state for particular geometrical parameters of the sample. The antidot occupation number $n_o$ is calculated as a function of related parameters and comparison with existing expressions for the saturation number $n_s$ and with experimental results is given. For a small radius of antidots a triangular vortex lattice is obtained, where some of the vortices are pinned by the antidots and some of them are located between them. Transition between the square pinned and triangular vortex lattices is given for different values of the applied field. The enhanced critical current at integer and rational matching fields is found, where the level of enhancement at given magnetic field directly depends on the vortex-occupation number of the antidots. For certain parameters of the antidot lattice and/or temperature the critical current is found to be larger for higher magnetic fields. Superconducting/normal $H-T$ phase boundary exhibits different regimes as antidots are made larger, and we transit from a plain superconducting film to a thin-wire superconducting network. Presented results are in good agreement with available experiments and suggest possible new experiments.