High-temperature superconductivity in single unit cell layer FeSe due to soft phonons in the interface layer of the SrTiO3 substrate

Using a microscopic model of lattice vibrations in the $\mathrm{STO}(001)$ substrate, an additional ${\mathrm{\ensuremath{\Omega}}}_s=50$ meV longitudinal optical (LO) interface mode is identified. The soft mode propagating mainly in the first $\mathrm{TiO}{}₂$ layer (``$O$ chains'') has stronger electron-phonon coupling to electron gas in FeSe than a well-known ${\mathrm{\ensuremath{\Omega}}}<sub>h</sub>=100$ meV hard mode. The coupling constant, critical temperature, and replica band are calculated. Although there exists a forward in the electron-phonon scattering peak, it is clearly not as sharp as assumed in recent theories (delta-function-like). The critical temperature is obtained by solution of the gap equation and agrees with the observed one. The corresponding electron phonon coupling constant $\ensuremath{\lambda}=0.23$. The quasiparticle normal state ``satellite'' in spectral weight is broad and its peak appears at frequency much higher than ${\mathrm{\ensuremath{\Omega}}}_s$ consistent with observations usually associated with ${\mathrm{\ensuremath{\Omega}}}_h$. Possible relation of the transversal counterpart of the surface LO soft mode with known phonons is discussed.