Title: Dipolar phonons and electronic screening in monolayer FeSe on SrTiO$_3$,
Abstract: Monolayer films of FeSe grown on SrTiO$_3$ substrates exhibit significantly
higher superconducting transition temperatures than those of bulk FeSe.
Interaction of electrons in the FeSe layer with dipolar SrTiO$_3$ phonons has
been suggested as the cause of the enhanced transition temperature. In this
paper we systematically study the coupling of SrTiO$_3$ longitudinal optical
phonons to the FeSe electron, including also electron-electron Coulomb
interactions at the random phase approximation level. We find that the
electron-phonon interaction between FeSe and SrTiO$_3$ substrate is almost
entirely screened by the electronic fluctuations in the FeSe monolayer, so that
the net electron-phonon interaction is very weak and unlikely to lead to
superconductivity.