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Superconductivity from repulsion in LiFeAs: novel s-wave symmetry and potential time-reversal symmetry breaking

We analyze the structure of the pairing interaction and superconducting gap in LiFeAs by decomposing the pairing interaction for various kz cuts into s- and d-wave components and by studying the leading superconducting instabilities. We use the ten orbital tight-binding model, derived from ab-initio LDA calculations with hopping parameters extracted from the fit to ARPES experiments. We find that the pairing interaction almost decouples between two subsets, one consists of the outer hole pocket and two electron pockets, which are quasi-2D and are made largely out of dxy orbital, and the other consists of the two inner hole pockets, which are quasi-3D and are made mostly out of dxz and dyz orbitals. Furthermore, the bare inter-pocket and intra-pocket interactions within each subset are nearly equal. In this situation, small changes in the intra-pocket and inter-pocket interactions due to renormalizations by high-energy fermions give rise to a variety of different gap structures. We find four different configurations of the s-wave gap immediately below Tc: the one in which superconducting gap changes sign between two inner hole pockets and between the outer hole pocket and two electron pockets, the one in which the gap changes sign between two electron pockets and three hole pockets, the one in which the gap on the outer hole pocket differs in sign from the gaps on the other four pockets, and the one in which the gaps on two inner hole pockets have one sign, and the gaps on the outer hole pockets and on electron pockets have different sign. Different s-wave gap configurations emerge depending on whether the renormalized interactions increase attraction within each subset or increase the coupling between particular components of the two subsets. We argue that the state with opposite sign of the gaps on the two inner hole pockets has the best overlap with ARPES data.