  SrTiO3 is known for its proximity to a ferroelectric phase and for showing an
'optimal' doping for superconductivity with a characteristic dome-like
behaviour 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 BCS 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 behaviour 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
Tc 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 SrTiO3.
