Electron-Phonon Couplings of the Interfacial Mode in FeSe Thin Films on SrTiO$_3$ and BaTiO$_3$

Monolayers FeSe on SrTiO$_3$ or BaTiO$_3$ substrates possess highest superconducting transition temperatures in Fe-based superconductors with $T_c\sim 70$ K measured by angle-resolved photoemission spectroscopy (ARPES) and other experiments. Furthermore, the high $T_c$'s concur with exact replica bands in ARPES spectra. A forward scattering mechanism with small momentum transfer through the electron-phonon interaction has been proposed to explain the high $T_c$'s and the replica bands.[1] We apply {\it ab initio} techniques to study such coupling in monolayer and bilayer FeSe thin films on SrTiO$_3$, BaTiO$_3$, and oxygen-vacant SrTiO$_3$ substrates. Our results confirm the forward scattering nature of electron-phonon coupling of the oxygen polar mode whose energy coincides with the off-set energy of the replica bands. [1]L.~Rademaker, et al., arXiv:1507.03967.