Theory of the Motion of Vortices in Superconductors

TLDR

The motion of vortex lines in type II superconductors is modeled by a local generalization of London theory, which is believed to accurately describe relatively pure superconductors (l > ξ₀) with vortex lines possessing normal cores. The model derives vortex motion from this local theory, treating the transport current J_T as comprising both superfluid and normal flow components. It predicts that a uniform transport current induces vortex motion that drives electric fields through the core, yielding a total current J_T + J₀(r − v_L t); the resulting viscosity and flow resistivity match empirical Kim laws, and the Hall angle in the mixed state equals that of the normal state at the core magnetic field.

Abstract

The theory of the motion of vortex lines in the mixed state of type II superconductors is derived on the basis of a local model that is a generalization of the London theory. It is believed the model simulates reasonably well the behavior of relatively pure superconductors ($l>{\ensuremath{\xi}}_{0}$), giving a vortex line with a normal core. It is found that if the force on a line is produced by a uniform transport current ${\mathrm{J}}_{T}$, electric fields generated by the motion drive the current through the core, so that the total current flow is ${\mathrm{J}}_{T}+{\mathrm{J}}_{0}(\mathrm{r}\ensuremath{-}{\mathrm{v}}_{L}t)$, where ${\mathbf{J}}_{0}$(r) is the circulation of a stationary vortex and ${\mathrm{v}}_{L}$ is the velocity of the line. In part ${\mathrm{J}}_{T}$ represents superfluid flow and in part normal flow. Expressions derived for the viscosity and flow resistivity are nearly identical with empirical laws of Kim and co-workers. The Hall angle expected in the mixed state is the same as in the normal state for a magnetic field equal to that in the core.