Theory of superconductivity mediated by soft polar modes in incipient ferroelectrics

Experimental evidence suggests that superconductivity in SrTiO3 is mediated by a soft transverse ferroelectric mode which, according to conventional theories, has negligible coupling with electrons. A phenomenological Rashba type coupling has been proposed on symmetry arguments but a microscopic derivation is lacking. Here we fill this gap and obtain a linear coupling directly from a minimal microscopic model of the electronic structure. We find that the effective electron-electron pairing interaction has a strong momentum dependence. This yields an unusual situation in which the leading s-wave channel is followed by a sub-leading p-wave state which shows a stronger pairing instability than the d-wave state. The bare Rashba coupling constant is estimated for the lowest band of doped SrTiO3 with the aid of first-principles computations and found to be much larger than previously thought. We argue that although for a uniform system the BCS coupling λ is small, it can produce the right order of magnitude for Tc in the presence of structural inhomogeneities. Finally, following an analogous method, we discuss the relevance of the quadratic coupling to the soft polar mode in this system.