Superconductivity in the two-dimensional electron gas induced by high-energy optical phonon mode and large polarization of the SrTiO3 substrate

Pairing in one-atomic-layer-thick two-dimensional electron gas (2DEG) by a single flat band of high-energy longitudinal optical phonons is considered. The polar dielectric SrTiO₃ (STO) exhibits such an energetic phonon mode and the 2DEG is created both when one unit cell FeSe layer is grown on its (100) surface and on the interface with another dielectric like LaAlO₃ (LAO). We obtain a quantitative description of both systems solving the gap equation for Tc for arbitrary Fermi energy εF, electron-phonon coupling λ, and the phonon frequency Ω, and direct (random-phase approximation) electron-electron repulsion strength α. The focus is on the intermediate region between the adiabatic, εF>>Ω, and the nonadiabatic, εF<<Ω, regimes. The high-temperature superconductivity in single-unit-cell FeSe/STO is possible due to a combination of three factors: high-longitudinal-optical phonon frequency, large electron-phonon coupling λ~0.5, and huge dielectric constant of the substrate suppression the Coulomb repulsion. It is shown that very low density electron gas in the interfaces is still capable of generating superconductivity of the order of 0.1 K in LAO/STO.