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(T) are much more efficient than those with a size close to xi(T). 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) approximate to 1), multiquanta vortex lattices (n(s)>1), and finally we have reached the limit of superconducting networks at n(s) much greater than 1.