Conditions for non-monotonic vortex interaction in two-band   superconductors
  We describe a semi-analytic approach to the two-band Ginzburg-Landau theory, which predicts the behavior of vortices in two-band superconductors. We show that the character of the short-range vortex-vortex interaction is determined by the sign of the normal domain - superconductor interface energy, in analogy with the conventional differentiation between type-I and type-II superconductors. However, we also show that the long-range interaction is determined by a modified Ginzburg-Landau parameter $\kappa^*$, different from the standard $\kappa$ of a bulk superconductor. This opens the possibility for non-monotonic vortex-vortex interaction, which is temperature-dependent, and can be further tuned by alterations of the material on the microscopic scale. 
A. Chaves, L. Komendov\'a, M. V. Milo\v{s}evi\'c, J. S. Andrade Jr.,   G. A. Farias and F. M. Peeters
cond-mat.supr-con