Time reversal symmetry breakdown in normal and superconducting states in frustrated three-band systems

We discuss the phase diagram and phase transitions in U(1)×Z₂ three-band superconductors with broken time reversal symmetry. We find that beyond mean-field approximation and for sufficiently strong frustration of interband interactions there appears an unusual metallic state precursory to a superconducting phase transition. In that state, the system is not superconducting. Nonetheless, it features a spontaneously broken Z₂ time reversal symmetry. By contrast, for weak frustration of interband coupling the energy of a domain wall between different Z₂ states is low and thus fluctuations restore broken time reversal symmetry in the superconducting state at low temperatures.