Superconductivity at low density near a ferroelectric quantum critical point: Doped SrTiO3
Abstract
Recent experiments on electron- or hole-doped SrTiO$_{3}$ have revealed a hitherto unknown form of superconductivity, where 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 fully dynamical treatment of the problem calling for (i) a systematic modeling of the dynamical screening of the Coulomb interaction by ionic and electronic charges and (ii) a transverse optical phonon mediated pair interaction. The model allows for a nearly parameter free calculation of the transition temperature as a function of both, the doping concentration and the dielectric properties of the host system. 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 to capture the effect of the incipient (or real) ferroelectric phase in pure, or oxygen isotope substituted SrTiO$_{3}$
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