Vortex dynamics in type II superconductors under strong pinning conditions

TL;DR

This paper investigates vortex dynamics in type II superconductors with strong pinning, revealing a shifted linear force-velocity relation and deriving Coulomb's dry friction law from vortex pinning effects.

Contribution

It provides a combined analytical and numerical analysis of vortex behavior under strong pinning, deriving the force-velocity characteristic and connecting it to dry friction laws.

Findings

Force-velocity characteristic is nearly linear and shifted by critical force-density.

Velocity-dependent average pinning-force density changes on a specific velocity scale.

Derivation of Coulomb's law of dry friction for strong vortex pinning.

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 $\langle F_p(v)\rangle$ 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 $F_c = \langle F_p(v=0)\rangle \propto n_p f_p$. 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.