Strong pinning regimes explored with large-scale Ginzburg-Landau simulations

Improving the current-carrying capability of superconductors requires a deep understanding of vortex pinning. Within the theory of (3D) strong pinning [1] an ideal vortex lattice is weakly deformed by a low density $n_p$ of strong defects. In this limit the critical current $j_c$ is expected to grow linearly with $n_p$ and to decrease with the field $B$ according to $B^{-\alpha}$ with $\alpha\approx 0.5$. In the small-field limit the (1D) strong pinning theory of isolated vortices predicts $j_c\propto n_p^{0.5}$, independent of $B$. We explore strong pinning by low defect densities using time-dependent Ginzburg-Landau simulations [2]. Our numerical results suggest the existence of a wide regime, where the lattice order is destroyed and yet interactions between vortices are important. In particular, for large defects we found an extended range of power-law decay of $j_c(B)$ with $\alpha\approx 0.3$, smaller than predicted. This regime requires the development of new analytical models. Exploring the behavior of $j_c$ for various defect densities and sizes, we will establish pinning regimes and applicability limits of the conventional theory. [1] G. Blatter {\it et al.}, Phys. Rev. Lett. {\bf 92}, 067009 (2004) [2] I. A. Sadovskyy {\it et al.}, J. Comput. Phys. {\bf 294}, 639 (2015)