Impact of Strong Forward Scattering Electron-Phonon Coupling at the SrTiO3 Interface

Recent experiments have demonstrated the importance of electron-phonon coupling strongly peaked at small momentum transfer in enhancing superconductivity and providing strong band renormalizations in both monolayer FeSe films on SrTiO$_3$ (STO) as well as bulk STO. This coupling to the LO$_4$ phonon in STO also was found to be sensitive to the screening of doped carriers in the surface state, whose shallow band bottom precludes perturbative treatment of the coupling. Using microscopic models and many-body algorithms, we characterize spectra and trends of superconductivity via a doping dependence of the effective electron-phonon coupling. We discuss our results in terms of the ratio of the lattice to kinetic energy and highlight the role of screening.