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Using the Ginzburg-Landau theory extended to the next-to-leading order wedetermine numerically the healing lengths of the two order parameters at thetwo-gap superconductor/normal metal interface. We demonstrate on severalexamples that those can be significantly different even in the strict domain ofapplicability of the Ginzburg-Landau theory. This justifies the use of thistheory to describe relevant physics of two-gap superconductors, distinguishingthem from their single-gap counterparts. The calculational degree of complexityincreases only slightly with respect to the conventional Ginzburg-Landauexpansion, thus the extended Ginzburg-Landau model remains numerically far lessdemanding compared to the full microscopic approaches.

Different length-scales for order parameters in two-gap superconductors: the extended Ginzburg-Landau theory