S+is state with broken time-reversal symmetry in Fe-based superconductors

We analyze the evolution of the superconducting gap structure in strongly hole-doped Ba_1-xK_xFe₂As₂ between x=1 and x∼0.4 (optimal doping). In the latter case, the pairing state is most likely s±, with different gap signs on hole and electron pockets, but with the same signs of the gap on the two Γ-centered hole pockets (a ++ state on hole pockets). In a pure KFe₂As₂ (x=1), which has only hole pockets, laser ARPES data suggested another s± state, in which the gap changes sign between hole pockets (a +- state). We analyze how a ++ gap transforms into a +- gap as x→1. We found that this transformation occurs via an intermediate s+is state in which the gaps on the two hole pockets differ in phase by, which gradually involves from =π (the +- state) to =0 (the ++ state). This state breaks time-reversal symmetry and has huge potential for applications. We compute the dispersion of collective excitations and show that two different Leggett-type phase modes soften at the two end points of the time-reversal-symmetry-breaking state.