Optimization of vortex pinning by nanoparticles using simulations of the time-dependent Ginzburg-Landau model

Abstract

Incorporating nanoparticles into superconducting materials has emerged as an efficient route to enhance their current-carrying capability. However, a thorough understanding of how these inclusions can be used in the most efficient way is still lacking. We address this problem of optimizing the vortex pinning landscape for randomly distributed metallic spherical inclusions using systematic large-scale numerical simulations of time-dependent Ginzburg-Landau equations. This approach allows us to predict the size and density of particles for which the highest critical current is realized. For a given particle size and magnetic field, the critical current reaches a maximum value at a particle density, which typically corresponds to 15%--23% of the total volume being replaced by the nonsuperconducting material. For a fixed diameter, this optimal particle density increases with the magnetic field. Moreover, we found that, as the magnetic field increased, the optimal particle diameter slowly decreases from 4.5 to 2.5 coherence lengths. This result shows that pinning landscapes have to be designed for specific applications taking into account relevant magnetic field scales.