Superconductivity mediated by ferroelectric fluctuations: anisotropic gap structure and possible application to SrTiO₃

SrTiO₃ is a semiconducting oxide that undergoes a phase transition to a superconducting state upon electron doping. Although such superconducting phase was first observed more than 50 years ago, its nature and origin remain an unsettled puzzle. Interestingly, recent experimental and theoretical works suggest an interplay between ferroelectricity and superconductivity in this material. Motivated by these studies, we study superconductivity mediated by odd-parity ferroelectric modes. We consider a Rashba-like coupling between the electrons and the ferroelectric fluctuations, which is possible due to the presence of spin-orbit coupling. We derive the effective pairing interaction and solve the resulting linearized gap equation away from quantum criticality. We find that the effective coupling, which is attractive in the singlet channel, is dominated by the soft transverse optical mode. Moreover, the superconducting gap is shown to develop an anisotropy that grows as the system approaches the ferroelectric phase. Finally, we discuss the competition with other even-parity superconducting channels and the possible application of our results to SrTiO₃.