Vortex dynamics in type II superconductors under strong pinning conditions

Abstract

We study effects of pinning on the dynamics of a vortex lattice in a type II superconductor in the strong-pinning situation and determine the force--velocity (or current--voltage) characteristic combining analytical and numerical methods. Our analysis deals with a small density $n_p$ of defects that act with a large force $f_p$ on the vortices, thereby inducing bistable configurations that are a characteristic feature of strong pinning theory. We determine the velocity-dependent average pinning-force density $⟨F_p(v)⟩$ and find that it changes on the velocity scale $v_p\sim f_p/\eta a_0^3$, where $\eta$ is the viscosity of vortex motion and $a_0$ the distance between vortices. In the small pin-density limit, this velocity is much larger than the typical flow velocity $v_c\sim F_c/\eta$ of the free vortex system at drives near the critical force-density $F_c=⟨F_p(v=0)⟩\propto n_p{f}_p$. As a result, we find a generic excess-force characteristic, a nearly linear force--velocity characteristic shifted by the critical force-density $F_c$; the linear flux-flow regime is approached only at large drives. Our analysis provides a derivation of Coulomb's law of dry friction for the case of strong vortex pinning.

24 pages, 12 figures

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