| Summary: | SrTiO_{3} is known for its proximity to a ferroelectric phase and for showing an “optimal” doping for superconductivity with a characteristic domelike behavior resembling systems close to a quantum critical point. Several mechanisms have been proposed to link these phenomena, but the abundance of undetermined parameters prevents a definite assessment. Here, we use ab initio computations supplemented with a microscopic model to study the linear coupling between conduction electrons and the ferroelectric soft transverse modes allowed in the presence of spin-orbit coupling. We find a robust Rashba-like coupling, which can become surprisingly strong for particular forms of the polar eigenvector. We characterize this sensitivity for general eigenvectors and, for the particular form deduced by hyper-Raman scattering experiments, we find a Bardeen-Cooper-Schrieffer pairing coupling constant of the right order of magnitude to support superconductivity. The ab initio computations enable us to go beyond the linear-in-momentum conventional Rashba-like interaction and naturally explain the dome behavior including a characteristic asymmetry. The dome is attributed to a momentum-dependent quenching of the angular momentum due to a competition between spin-orbit and hopping energies. The optimum density for having maximum T_{c} results in rather good agreement with experiments without free parameters. These results make the generalized Rashba dynamic coupling to the ferroelectric soft mode a compelling pairing mechanism to understand bulk superconductivity in doped SrTiO_{3}.
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