Longitudinal currents in a system of Abrikosov vortices

A current along the vortices is allowed by the Ginzburg-Landau equations. It arises as a response of the vortex system to some special external conditions. Macroscopically, it represents an internal degree of freedom of this system in addition to other possible reactions (displacement, bending) to external perturbations. Longitudinal currents are maximum on the sample surface and attenuate exponentially with depth $\Lambda =\lambda {(1-\frac{H}{H_{c2\mathrm{}}})}^{-\frac{1}{2}}$ ($\lambda$ is the penetration depth, $\frac{H}{H_{c2\mathrm{}}}\sim 1$). Implications of these currents for the macroscopic theory and a possibility to observe them are discussed.