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 the 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 interpocket and intrapocket interactions within each subset are nearly equal. In this situation, small changes in the intrapocket and interpocket interactions due to renormalizations by high-energy fermions give rise to a variety of different gap structures. We focus on s-wave pairing which, as experiments show, is the most likely pairing symmetry in LiFeAs. We find four different configurations of the s-wave gap immediately below Tc: one in which the superconducting gap changes sign between two inner hole pockets and between the outer hole pocket and two electron pockets, one in which the gap changes sign between two electron pockets and three hole pockets, one in which the gap on the outer hole pocket differs in sign from the gaps on the other four pockets, and 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 discuss the phase diagram and experimental probes to determine the structure of the superconducting gap in LiFeAs. We argue that the state with opposite sign of the gaps on the two inner hole pockets has the best overlap with ARPES data. We also argue that at low T, the system may enter into a "mixed" s+is state, in which the phases of the gaps on different pockets differ by less than π and time-reversal symmetry is spontaneously broken.