Charge transfer effect of FeSe thin films on SrTiO$_3$

Monolayer FeSe grown on SrTiO$_3$ substrate has shown a significant enhancement in the superconducting transition temperature (T$_c$) relative to the bulk material. Monolayers of FeSe are electron doped relative to bulk; we propose that the doping comes from work-function-mismatch driven charge transfer from SrTiO$_3$ impurity bands, modified by out-of-plane polar distortions of the SrTiO$_3$. We present a modified Schottky model combined with density functional calculations substantiating this picture for monolyaer FeSe films on Nb doped SrTiO$_3$. Physically relevant levels of Nb doping are shown to lead to doping of the FeSe compatible with observation. Adding polar fluctuations to the model leads to an electron-phonon interaction whose effect on the transition temperature is investigated.