Recent experiments on electron- or hole-doped SrTiO3 have revealed a hitherto unknown form of superconductivity in which the Fermi energy of the paired electrons is much lower than the energies of the bosonic excitations thought to be responsible for the attractive interaction. We show that this situation requires a fresh look at the problem, calling for (i) a systematic modeling of the dynamical screening of the Coulomb interaction by ionic and electronic charges, (ii) a transverse optical phonon mediated pair interaction, and (iii) a determination of the energy range over which the pairing takes place. We argue that the latter is essentially given by the limiting energy beyond which quasiparticles cease to be well-defined. The model allows us to find the transition temperature as a function of both the doping concentration and the dielectric properties of the host system, in good agreement with experimental data. The additional interaction mediated by the transverse optical soft phonon is shown to be essential in explaining the observed anomalous isotope effect. The model allows us to capture the effect of the incipient (or real) ferroelectric phase in pure or oxygen isotope substituted SrTiO3.
Physical Review B