Soft phonons in the interface layer of the STO substrate can explain high temperature superconductivity in one unit cell FeSe

Using a microscopic model of lattice vibrations in the STO(001) substrate, an additional 50 mev longitudinal optical (LO) interface mode is identified. The soft mode propagating mainly in the first TiO2 layer ("O chains") has stronger electron - phonon coupling to electron gas in FeSe than a well known 100 mev hard mode. The coupling constant, critical temperature, 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 satellite is broad and its peak appears at frequency much higher than the phonon frequency consistent with observations. Possible relation of the transverse counterpart of the surface LO soft mode with known phonons is discussed.