Theory and simulations on strong pinning of vortex lines by nanoparticles

The pinning of vortex lines by an array of nanoparticles embedded inside superconductors has become the most efficient practical way to achieve high critical currents. In this scenario, pinning occurs via trapping of the vortex-line segments, and the critical current is determined by the typical length of the trapped segments. To verify analytical estimates and develop a quantitative description of strong pinning, we numerically simulated isolated vortex lines driven through an array of nanoparticles. We found that the critical force grows roughly as the square root of the pin density and that it is strongly suppressed by thermal noise. The configurations of pinned lines are strongly anisotropic; displacements in the drive directions are much larger than those in the transverse direction. Moreover, we found that the roughening index for the longitudinal displacements exceeds 1. This indicates that the local stresses in the critical region increase with the total line length and that the elastic description breaks down in the thermodynamic limit. Thermal noise reduces the anisotropy of displacements in the critical regions and straightens the lines.