Pinning size effects in critical currents of superconducting films

The thickness dependence of the critical current density J c ( d ) in films due to the two-dimensional–three-dimensional (2D–3D) pinning crossover at low magnetic fields is addressed, taking into account the spatial correlation of pinning centres, the combined effect of bulk and surface pinning, and the effect of thermal fluctuations. The whole J c ( d ) curve for both the 3D and 2D pinning regimes, and the crossover thickness d c are calculated using a dynamic approach for a random pinning potential characterized by the Gaussian correlation functions. It is shown that the spatial correlation of pinning centres can significantly increase d c as compared to uncorrelated point pins, and the competition between pinning and thermal fluctuations gives rise to a nonmonotonic dependence of J c ( d ). The account of multiscale spatial correlations in a uniform pinning nanostructure can result in behaviour of J c ( d ) similar to that observed on YBa 2 Cu 3 O 7−δ . The ultimate limit of J c is discussed.