Two-band superconductors near Tc
The Ginzburg-Landau (GL) equations for two-band clean s-wave superconductors have been derived from the microscopic weak-coupling formalism with a general 2x2 coupling potentials (Ref.[2]). It is shown here that within the GL approximation the ratio of the order parameters Delta_1(r,T)/Delta_2(r,T) is an interaction dependent constant. This implies that within the GL domain, the length scales for spacial variation of both order parameters are the same and, in particular, that they have the same phase in equilibrium (modulo \pi). Along with a single length scale for the magnetic field change, this amounts to a single physical GL parameter kappa. In other words, a two-band superconductor near Tc is described by a single complex order parameter.