Peak effect at the weak- to strong pinning crossover

TL;DR

This paper investigates the transition from weak to strong vortex pinning in type-II superconductors, revealing a peak effect in the critical current density as defect strength surpasses a critical threshold.

Contribution

It introduces a Landau expansion approach to model the weak- to strong pinning crossover and predicts a peak effect in the critical current density.

Findings

Identifies a sharp rise in critical current at the crossover

Derives a quadratic dependence of the peak effect on defect strength

Provides a theoretical framework for vortex pinning transitions

Abstract

In type-II superconductors, the magnetic field enters in the form of vortices; their flow under application of a current introduces dissipation and thus destroys the defining property of a superconductor. Vortices get immobilized by pinning through material defects, thus resurrecting the supercurrent. In weak collective pinning, defects compete and only fluctuations in the defect density produce pinning. On the contrary, strong pins deform the lattice and induce metastabilities. Here, we focus on the crossover from weak- to strong bulk pinning, which is triggered either by increasing the strength $f_\mathrm{p}$ of the defect potential or by decreasing the effective elasticity of the lattice (which is parametrized by the Labusch force $f_\mathrm{Lab}$). With an appropriate Landau expansion of the free energy we obtain a peak effect with a sharp rise in the critical current density $j_\mathrm{c} \sim j_0 (a_0\xi^2 n_p) (\xi^2/a_0^2) (f_\mathrm{p}/f_\mathrm{Lab} -1)^2$.