Phonon linewidth due to electron-phonon interactions with strong forward scattering in FeSe thin films on oxide substrates

The discovery of an enhanced superconducting transition temperature T_c in monolayers of FeSe grown on several oxide substrates has opened a different route to high-T_c superconductivity through interface engineering. One proposal for the origin of the observed enhancement is an electron-phonon interaction across the interface that is peaked at small momentum transfers. Here, we examine the implications of such a coupling on the phononic properties of the system. We find that while a strong forward scattering leads to a sizable broadening of phonon lineshape, which may result in charge instabilities at long-wavelengths, the inclusion of Coulombic screening significantly reduces the phonon broadening, thus explaining the lack of anomalously broad phonon linewidths in the FeSe interface systems as shown by experiments. We also show in what parameter range and conditions, the T_c enhancement and the replica band feature in the electron spectral function can persist with the screened electron-phonon coupling in the forward scattering direction.