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 T-c for arbitrary Fermi energy is an element of(F), electron-phonon coupling lambda, and the phonon frequency Omega, and direct (random-phase approximation) electron-electron repulsion strength alpha. The focus is on the intermediate region between the adiabatic, is an element of(F) >> Omega, and the nonadiabatic, is an element of(F) << Omega, 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 lambda similar to 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.