Pairng with an incipient band with enhanced T_C from forward scattering phonons.

The discovery of a mono-layer FeSe grown on STO substrate as well as other intercalated layered Fe-based superconductors raised questions regarding the validity of spin fluctuation pairing in these materials. Because theses systems show hole bands several 10 meV below the Fermi-level, it may seem that spin fluctuation exchange is not the primary contributor for the pairing. Here, we utilize fully self-consistent Fluctuation-exchange (FLEX) approximations in a bilayer Hubbard model to demonstrate the superconductivity can still appear from spin fluctuation exchange between an electron pocket and an incipient hole band. The resulting spectral function shows an s-wave superconducting gap opening at the Fermi-level centering at the electron band; at the same time, additional spectral weights appearing what seems to be a mirror of the hole band (mirror band) above the Fermi-level. In addition, the simulation has also considered the intra-orbital, attractive electron-phonon interactions with a strong forward scattering limit. The preliminary result has shown a larger enhancement in T_C suggesting that such a type of phonons can coexist with the S± paring that arises from the spin fluctuation pairing.