Designing high-performance superconductors with nanoparticle inclusions: Comparisons to strong pinning theory

One of the most promising routes for achieving high critical currents in superconductors is to incorporate dispersed, non-superconducting nanoparticles to control the dissipative motion of vortices. However, these inclusions reduce the overall superconducting volume and can strain the interlaying superconducting matrix, which can detrimentally reduce T$_{c}$. Consequently, an optimal balance must be achieved between the nanoparticle density n$_{p}$ and size d. Determining this balance requires garnering a better understanding of vortex–nanoparticle interactions, described by strong pinning theory. Here, we map the dependence of the critical current on nanoparticle size and density in (Y$_{0.77}$, Gd$_{0.23}$)Ba$_{2}$Cu$_{3}$O$_{7−δ}$ films in magnetic fields of up to 35 T and compare the trends to recent results from time-dependent Ginzburg–Landau simulations. We identify consistency between the field-dependent critical current J$_{c}$ (B) and expectations from strong pinning theory. Specifically, we find that J$_{c}$ ∝ B$^{−α }$, where α decreases from 0.66 to 0.2 with increasing density of nanoparticles and increases roughly linearly with nanoparticle size d/ξ (normalized to the coherence length). ... mehrAt high fields, the critical current decays faster (∼B$^{Z-1}$), suggesting that each nanoparticle has captured a vortex. When nanoparticles capture more than one vortex, a small, high-field peak is expected in Jc(B). Due to a spread in defect sizes, this novel peak effect remains unresolved here. Finally, we reveal that the dependence of the vortex creep rate S on nanoparticle size and density roughly mirrors that of α, and we compare our results to low-T nonlinearities in S(T) that are predicted by strong pinning theory.