Strong-pinning regimes by spherical inclusions in anisotropic type-II superconductors

TL;DR

This study uses large-scale simulations to analyze how spherical inclusions in anisotropic type-II superconductors influence vortex pinning and critical current behavior, revealing regimes of strong pinning and the effects of inclusion size and density.

Contribution

It provides new insights into vortex pinning mechanisms by spherical inclusions, extending strong-pinning theory to account for multiple vortex trapping and disordered lattice regimes.

Findings

Critical current decays as B^{-0.66} for low inclusion density.

Higher inclusion density leads to more disordered vortex lattices.

Large inclusions can trap multiple vortices, affecting the critical current peak.

Abstract

The current-carrying capacity of type-II superconductors is decisively determined by how well material defect structures can immobilize vortex lines. In order to gain deeper insights into the fundamental pinning mechanisms, we have explored the case of vortex trapping by randomly distributed spherical inclusions using large-scale simulations of the time-dependent Ginzburg-Landau equations. We find that for a small density of particles having diameters of two coherence lengths, the vortex lattice preserves its structure and the critical current $j_c$ decays with the magnetic field following a power-law $B^{-\alpha}$ with $\alpha \approx 0.66$, which is consistent with predictions of strong-pinning theory. For a higher density of particles and/or larger inclusions, the lattice becomes progressively more disordered and the exponent smoothly decreases down to $\alpha \approx 0.3$. At high magnetic fields, all inclusions capture a vortex and the critical current decays faster than $B^{-1}$ as would be expected by theory. In the case of larger inclusions with a diameter of four coherence length, the magnetic-field dependence of the critical current is strongly affected by the ability of inclusions to capture multiple vortex lines. We found that at small densities, the fraction of inclusions trapping two vortex lines rapidly grows within narrow field range leading to a peak in $j_c(B)$-dependence within this range. With increasing inclusion density, this peak transforms into a plateau, which then smooths out. Using the insights gained from simulations, we determine the limits of applicability of strong-pinning theory and provide different routes to describe vortex pinning beyond those bounds.