Interaction of vortices in type II superconductors and the behavior nearH c1 at arbitrary temperature

The interaction between well-separated Abrikosov vortices is calculated using Eilenberger's version of the Gorkov theory. Let λ and ξ be the decay lengths determining the asymptotic behavior of the magnetic field and the order parameter for an isolated vortex. Then the onset of attraction in the limit of large vortex separation is either given by λ=ξ or by λ becoming complex, whichever occurs first. It is shown that in general a first order transition atH _c1 takes place already in the region of asymptotic repulsion because of the appearance of a minimum in the interaction energy at finite vortex separation.