Ginzburg-Landau theory of two-band superconductors: Absence of type-1.5 superconductivity

It is shown that within the Ginzburg-Landau (GL) approximation the order parameters ${\Delta }_1(\mathbf{r},T)$ and ${\Delta }_2(\mathbf{r},T)$ in two-band superconductors vary on the same length scale, the difference in zero-$T$ coherence lengths ${\xi }_{0\nu }~\hslash v_{F\nu }/{\Delta }_{\nu }(0)$, $\nu =1,2$ notwithstanding. This amounts to a single physical GL parameter $\kappa$ and the classic GL dichotomy: $\kappa <1/\sqrt{2}$ for type I and $\kappa >1/\sqrt{2}$ for type II.