Conditions for nonmonotonic vortex interaction in two-band superconductors

We describe a semianalytic 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 ${\ensuremath{\kappa}}^{*}$, different from the standard $\ensuremath{\kappa}$ of a bulk superconductor. This opens the possibility for nonmonotonic vortex-vortex interaction, which is temperature dependent, and can be further tuned by alterations of the material on the microscopic scale.