Dynamical Aspects of Strong Pinning of Magnetic Vortices in Type-II Superconductors

We determine the current-voltage characteristic of type-II superconductors in the presence of strong pinning centers. Focusing on a small density of defects, we derive a generic form for the characteristic with a linear flux-flow branch shifted by the critical current (excess-current characteristic). The details near onset, a hysteretic jump (for $\kappa \gg 1$) or a smooth velocity turn-on ($\kappa \to 1$), depend on the Labusch parameter $\kappa$ characterizing the pinning centers. Pushing the single-pin analysis into the weak pinning domain, we reproduce the collective pinning results for the critical current.

Figure 1

Average pinning force $⟨f_p⟩$ for a Lorentzian-shaped pinning potential of various strengths. For strong pinning $\kappa \gg 1$ the critical force $f_c$ is large and the pinning force decays monotonically. On approaching the Labusch point $\kappa \to 1$ the critical force $f_c$ vanishes and the pinning force is nonmonotonic, first increasing $\propto \sqrt{v}$ and then decaying $\propto 1/\sqrt{v}$.

Figure 2

Force-velocity characteristic for a Lorentzian-shaped pinning potential. For small defect densities $n_p{a}_0{\xi }^2\kappa =0.05$ we find an excess-current characteristic, a shifted (by $F_c\propto n_p$) linear curve with a slope reflecting flux-flow behavior and approaching the true (unshifted) flux-flow behavior only at high velocities $v>\kappa v_{\mathrm{th}}\gg v_c$. The insets sketch the behavior near critical, with a hysteretic jump of order $v_{\mathrm{nl}}\propto n_p^2$ appearing at strong pinning $\kappa \gg 1$ and a smooth onset $v\propto v_{\mathrm{th}}(\kappa -1{)}^4(F_L/F_c-1{)}^2$ on approaching the Labusch point $\kappa \to 1$.