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

We study the electron-phonon coupling strength near the interface of monolayer and bilayer FeSe thin films on SrTiO$_3$, BaTiO$_3$, and oxygen-vacant SrTiO$_3$ substrates, using ab initio methods. The calculated total electron-phonon coupling strength $\lambda=0.2\text{--}0.3$ cannot account for the high $T_c\sim 70$ K observed in these systems through the conventional 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 this mode coincides with the offset energy of the replica bands measured recently by angle-resolved photoemission spectroscopy experiments. But the integrated coupling strength for this mode from our current calculations is still too small to produce the observed high $T_c$, even through the more efficient pairing mechanism provided by the forward scattering. We arrive at the same qualitative conclusion when considering a checkerboard antiferromagnetic configuration in the Fe layer. In light of the experimental observations of the replica band feature and the relatively high $T_c$ of FeSe monolayers on polar substrates, our results point towards a cooperative role for the electron-phonon interaction, where the cross-interface interaction acts in conjunction with a purely electronic interaction. We also discuss a few scenarios where the coupling strength obtained here may be enhanced.