# Interface Energy of Two-band Superconductors

Fig. 1. Interface energy between a normal and superconducting region at the coexistence magnetic field as function of the ratio of the penetration and coherence length. Positive (negative) values imply Type I (II) superconductivity.

There two major types of superconductor—Type-I, where the penetration depth of the magnetic field is shorter than the length scale of spatial variation of the superfluid density (the density of paired carriers) and Type-II, the opposite relation of these two lengths. Whether a specific system is of Type I or Type II has, in the past, been determined by the sign of the interface energy, , between coexisting superconducting and normal states. Most materials of practical importance are Type-II, so the existing classification is not only of an academic interest. It turns out the majority of newly discovered superconductors have two or more distinct pieces of the Fermi surface (two or more types of carriers), MgB2 is a famous example. The ongoing debate within the superconducting phenomenology community is how to classify such multi-band materials—Type I or Type II or something other than these two. We show that even for two bands, the two order parameters (proportional to densities of two paired carriers) vary on the same length scale, i.e., the classic Type-I or Type-II dichotomy holds also for two-band materials, see Fig. 1. Here, we plot the surface energy as a function of , the ratio of the penetration depth and the superconducting coherence length. We show numerically and analytically that is determined by the same universal function, , as in single band superconductors (see Fig. 1). Thus, we take the conservative position in the debate.

- Jani Geyer, Rafael M. Fernandes, V. G. Kogan, and Jörg Schmalian.
**Interface energy of two-band superconductors**.*Physical Review B***82**, 104521, (2010) DOI: 10.1103/PhysRevB.82.104521

Contact: V. G. Kogan, kogan@ameslab.gov

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