Back to mechanisms of superconductivity in low-doped strontium titanate
  We have analyzed two mechanisms proposed recently for superconductivity in doped SrTiO3 - the plasmon-mediated pairing and the potential of an instantaneous attraction between two electrons that owes its origin to the exchange by high-frequency optical phonons. The first approach seems to be self-consistent, but in a limited range of the dielectric constant. As to the direct instantaneous interaction between two electrons,it was hypothesized as due to the exchange by the band LO phonons. The latter supposition was incorrect. In the current paper, it shows that the contributions into the pairing matrix element possessing the structure of a net attraction come about only as the result of disorder. Indeed, the experiment revealed the mobility edge in doped SrTiO3. Doped electrons occupying states with the energy below the mobility edge are localized on dopants thereby become strongly coupled with the lattice vibrations. The emergence of the localized phonon modes attached to defect is one of the results of such electron-lattice coupling. For two electrons in the conduction band the virtual exchange by the quantum of such local mode manifests itself as the effective attraction. The total contribution into the pairing matrix element from these processes, increasing with concentration can overwhelm the Coulomb repulsion screened by the band LO phonons. That is, the role previously ascribed to the band LO phonons actually belongs to the localized phonons. 
Lev P. Gor'kov
cond-mat.supr-con