Interaction between moving Abrikosov vortices in type-II superconductors

The self-energy of a moving vortex is shown do decrease with increasing velocity. The interaction energy of two parallel slowly moving vortices differs from the static case by a small term $\propto v^2$; the “slow” motion is defined as having the velocity $v<v_c=c^2\mathrm{/}4\pi \sigma \lambda$, where $\sigma (T)$isconductivityofthenormalexcitationsand$\lambda (T)$ is London penetration depth. For higher velocities, $v>v_c(T)$, the interaction energy of two vortices situated along the velocity direction is enhanced and along the perpendicular direction is suppressed compared to the static case.