Pinning by an antidot lattice: The problem of the optimum antidot size

Critical current densities ${(j}_c)$ and pinning forces ${(f}_p)$ in superconducting Pb/Ge multilayers and single WGe films are strongly enhanced by introducing regular arrays of submicron holes (“antidot lattices”) acting as artificial pinning centers. Comparative measurements of $j_c$ and $f_p$ for several well-defined antidot diameters $D$ have shown that pinning centers with a size considerably larger than the temperature-dependent coherence length $\xi \mathrm{}\left(T\right)\mathrm{}$ are much more efficient than those with a size close to $\xi \mathrm{}\left(T\right).$ Moreover, the antidot size realizing the optimum pinning is field-dependent: we need smaller antidots to optimize pinning in lower fields and larger antidots for optimum pinning in higher fields. Crossover between different pinning regimes is controlled by the saturation number $n_s$ that defines the largest possible number of flux lines trapped by an antidot. In dependence upon the $n_s$ value, we have observed various composite flux lattices with vortices at antidots and interstices ${(n}_s\approx 1),$ multiquanta vortex lattices ${(n}_s>1),$ and finally we have reached the limit of superconducting networks at $n_s\gg 1.$