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 np of defects that act with a large force fp 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 〈Fp(v)〉 and find that it changes on the velocity scale vp∼fp/ηa03, where η is the viscosity of vortex motion and a0 the distance between vortices. In the small pin-density limit, this velocity is much larger than the typical flow velocity vc∼Fc/η of the free vortex system at drives near the critical force density Fc=〈Fp(v=0)〉∝npfp. As a result, we find a generic excess-force characteristic, a nearly linear force-velocity characteristic shifted by the critical force density Fc; 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.

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