The effects of Coulomb interactions on the superconducting gaps in iron-based superconductors

Recent angle-resolved photoemission spectroscopy measurements of Co-doped LiFeAs report a large and robust superconducting gap on the $\Gamma$-centered hole band that lies 8 meV below the Fermi level. We show that, unlike a conventional superconductor described by BCS theory, a multiband system with strong interband Coulomb interactions can explain these observations. We model LiFeAs with a five-band model in which the shallow hole band is coupled with the other bands by only Coulomb interactions. Using Eliashberg theory, we find reasonable interaction parameters that reproduce the $T_c$ and all five gaps of LiFeAs. The energy independence of the Coulomb interactions then ensures the robustness of the gap induced on the shallow band. Furthermore, due to the repulsive nature of the Coulomb interactions, the gap changes sign between the shallow band and the other hole pockets, corresponding to an unconventional $s_{\pm}$ gap symmetry. Unlike other families of iron-based superconductors, the gap symmetry of LiFeAs has not been ascertained experimentally. The experimental implications of this sign-changing state are discussed.