Vortex dynamics in type-II superconductors under strong pinning conditions

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(upsilon)> and find that it changes on the velocity scale upsilon(p) similar to 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 upsilon(c) similar to F-c/eta of the free vortex system at drives near the critical force density F-c = < F-p(upsilon = 0)> alpha 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.