Phonon mechanism in the most dilute superconductor n-type SrTiO3

Superconductivity of n-doped SrTiO3, which remained enigmatic for half a century, is treated as a particular case of nonadiabatic phonon pairing. Motivated by experiment, we suggest the existence of the mobility edge at some dopant concentration. The itinerant part of the spectrum consists of three conduction bands filling by electrons successively. Each subband contributes to the superconducting instability and exhibits a gap in its energy spectrum at low temperatures. We argue that superconductivity of n-doped SrTiO3 results from the interaction of electrons with several longitudinal (LO) optical phonons with frequencies much larger than the Fermi energy. Immobile charges under the mobility edge threshold increase the "optical" dielectric constant far above that in clean SrTiO3 placing control on the electron-LO phonon interaction. TC initially grows as density of states at the Fermi surface increases with doping, but the accumulating charges reduce the electrons-polar-phonon interaction by screening the longitudinal electric fields. The theory predicts maxima in the TC-concentration dependence indeed observed experimentally. Having reached a maximum in the third band, the transition temperature finally decreases, rounding out the TC (n) dome, the three maxima with accompanying superconducting gaps emerging consecutively as electrons fill successive bands. This arises from attributes of the LO optical phonon pairing of electrons. The mechanism of LO phonons opens the path to increasing superconducting transition temperature in bulk transition-metal oxides and other polar crystals, and in charged 2D layers at the LaAaO3/SrTiO3 interfaces and on the SrTiO3 substrates.