Time-reversal symmetry-breaking nematic superconductivity in FeSe

FeSe is a unique member of the family of iron-based superconductors, not only because of the high values of $T_{c}$ in FeSe monolayer, but also because in bulk FeSe superconductivity emerges inside a nematic phase without competing with long-range magnetic order. Near $T_{c}$, superconducting order necessarily has $s+d$ symmetry, because nematic order couples linearly the $s$-wave and $d$-wave harmonics of the superconducting order parameter. Here we argue that the near-degeneracy between $s$-wave and $d$-wave pairing instabilities in FeSe, combined with the sign-change of the nematic order parameter between hole and electron pockets, allows the superconducting order to break time-reversal symmetry at a temperature $T^{*}<T_{c}$. The transition from an $s+d$ state to an $s+\mathrm{e}^{i\alpha}d$ state should give rise to a peak in the specific heat and to the emergence of a soft collective mode that can be potentially detected by Raman spectroscopy.