Time-reversal symmetry broken metallic states in multiband superconductors

The recent discovery of so-called multiband superconductors, like the iron pnictides, has spurred a surge in interest for superconductors with several bands crossing the Fermi level. The reason for this is that frustration in interband couplings may lead to a broken $Z_2$ (``time reversal'') symmetry in addition to the ``ordinary'' breaking of the $\mathrm{U}(1)$ symmetry in single band superconductors, opening up for the possibility of new forms of topological excitations and interesting new physics. We have investigated phase diagrams and phase transitions of $\mathrm{U}(1)\times Z_2$ superconductors in 2D and 3D beyond mean-field approximation, using large-scale Monte Carlo simulations. In addition to the superfluid $\mathrm{U}(1)\times Z_2$ and $\mathrm{U}(1)$ broken states, we find, in a certain parameter regime, a new, non-superfluid (metallic) $Z_2$ broken (but $\mathrm{U}(1)$ symmetric) state where time-reversal symmetry is spontaneously broken.