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We study the electron-phonon coupling strength near the interface ofmonolayer and bilayer FeSe thin films on SrTiO$_3$, BaTiO$_3$, andoxygen-vacant SrTiO$_3$ substrates, using ab initio methods. The calculatedtotal electron-phonon coupling strength $\lambda=0.2\text{--}0.3$ cannotaccount for the high $T_c\sim 70$ K observed in these systems through theconventional phonon-mediated pairing mechanism. In all of these systems,however, we find that the coupling constant of a polar oxygen branch peaks at$\mathbf{q}=0$ with negligible coupling elsewhere, while the energy of thismode coincides with the offset energy of the replica bands measured recently byangle-resolved photoemission spectroscopy experiments. But the integratedcoupling strength for this mode from our current calculations is still toosmall to produce the observed high $T_c$, even through the more efficientpairing mechanism provided by the forward scattering. We arrive at the samequalitative conclusion when considering a checkerboard antiferromagneticconfiguration in the Fe layer. In light of the experimental observations of thereplica band feature and the relatively high $T_c$ of FeSe monolayers on polarsubstrates, our results point towards a cooperative role for theelectron-phonon interaction, where the cross-interface interaction acts inconjunction with a purely electronic interaction. We also discuss a fewscenarios where the coupling strength obtained here may be enhanced.

Ab initio Study of Cross-Interface Electron-Phonon Couplings in FeSe Thin Films on SrTiO$_3$ and BaTiO$_3$