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.