The origin of the high-temperature superconducting state observed in FeSe thin films, whose phase diagram displays no sign of magnetic order, remains a hotly debated topic. Here we investigate whether fluctuations arising due to the proximity to a nematic phase, which is observed in the phase diagram of this material, can promote superconductivity. We find that nematic fluctuations alone promote a highly degenerate pairing state, in which both $s$-wave and $d$-wave symmetries are equally favored, and $T_c$ is consequently suppressed. However, the presence of a sizable spin-orbit coupling or inversion symmetry breaking at the film interface lifts this harmful degeneracy and selects the $s$-wave state, in agreement with recent experimental proposals. The resulting gap function displays a weak anisotropy, which agrees with experiments in monolayer FeSe and intercalated ${\mathrm{Li}}_{1-x}(\mathrm{OH}{)}_x\text{FeSe}$.

• Received 8 June 2016

DOI:https://doi.org/10.1103/PhysRevLett.117.217003