Phonon Boost Effect on the S-wave Superconductor with Incipient Band.

We showed that the all phonons - not only forward-scattering phonon but also local (all-momentum-scattering) phonon - contribute to boosting Tc of the S-wave pairing state in the incipient band model. In particular, when the incipient band sinks deeper, the phonon boost effect of the local phonon increases and becomes as effective as the one of the forward-scattering phonon. Our finding implies that all interface phonons from the SrTiO substrate - not only the 90 meV Fuchs-Kliewer (F-K) phonon but also the 60 meV F-K phonon - as well as all intrinsic phonons of the FeSe monolayer itself, regardless of their degree of "forwardness", should contribute to increase Tc of the FeSe/STO monolayer system. This all-phonon boost mechanism should universally work in all heavily doped (either by holes or by electrons) Iron-based superconductors.