Three-band superconductivity and the order parameter that breaks time-reversal symmetry

We consider a model of multiband superconductivity, inspired by iron pnictides, in which three bands are connected via repulsive pair-scattering terms. Generically, three distinct superconducting states arise within such a model. Two of them are straightforward generalizations of the two-gap order parameter while the third one corresponds to a time-reversal symmetry-breaking order parameter, altogether absent within the two-band model. Potential observation of such a genuinely frustrated state would be a particularly vivid manifestation of the repulsive interband interactions being at the root of iron-based high-temperature superconductivity. We construct the phase diagram of this model and discuss its relevance to the iron pnictides family of high-temperature superconductors. We also study the case of the Josephson coupling between a two-band s^' or s± superconductor and a single-gap s-wave superconductor and the associated phase diagram.