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

TL;DR

This study investigates how nanoparticle size and density influence the critical current in superconductors, comparing experimental results with strong pinning theory to optimize vortex pinning without compromising superconducting properties.

Contribution

It provides a detailed mapping of critical current dependence on nanoparticle parameters and validates strong pinning theory predictions in high-field superconductors.

Findings

Critical current $J_c$ decreases with magnetic field as $B^{-eta}$, with $eta$ decreasing as nanoparticle density increases.

Critical current decay rate approaches $B^{-1}$ at high fields, indicating vortex capture by nanoparticles.

Vortex creep rate $S$ correlates with nanoparticle size and density, aligning with strong pinning theory predictions.

Abstract

One of the most promising routes for achieving unprecedentedly 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$_{7-\delta}$ films in magnetic fields up to 35 T, and compare the trends to recent results from time-dependent Ginzburg-Landau simulations. We identify consistencies between the field-dependent critical current $J_c(B)$ and expectations from strong pinning theory. Specifically, we find that that $J_c \propto B^{-\alpha}$, where $\alpha$ decreases from $0.66$ to $0.2$ with increasing density of nanoparticles and increases roughly linearly with nanoparticle size $d/\xi$ (normalized to the coherence length). At high fields, the critical current decays faster ($\sim B^{-1}$), suggestive that each nanoparticle has captured a vortex. When nanoparticles capture more than one vortex, a small, high-field peak is expected in $J_c(B)$. Due to a spread in defect sizes, this novel peak effect remains unresolved here. Lastly, we reveal that the dependence of the vortex creep rate $S$ on nanoparticle size and density roughly mirrors that of $\alpha$, and compare our results to low-$T$ nonlinearities in $S(T)$ that are predicted by strong pinning theory.