Flux flow in nearly pure low-κsuperconductors

A theory of flux flow useful for low-$\kappa$ superconductors is given where the electrodynamics is nonlocal. Fields and chemical potential gradients are induced by a transport current which causes the vortex to move with velocity ${\overrightarrow{\mathrm{v}}}_L$. These are determined self-consistently by the requirement that they generate a supercurrent to correspond to the displacement of a static vortex and compensate for scattering of thermally excited quasiparticles. Making use of an approximate analytic solution for a static vortex by Kramer and Pesch, it is shown that for the case of pure ($l\gg {\xi }_0$) superconductors at low temperatures ($T\lesssim 0.5T_c$) there is no backflow. The component of ${\overrightarrow{\mathrm{v}}}_L$ in the direction of the transport current is the transport velocity, a result of the Hall effect on the bound states in the vortex core.