Critical doping for the onset of a two-band superconducting ground state   in SrTiO$_{3-\delta}$
  In doped SrTiO$_{3}$ superconductivity persists down to an exceptionally low concentration of mobile electrons. This restricts the relevant energy window and possible pairing scenarios. We present a study of quantum oscillations and superconducting transition temperature, $T_{c}$ as the carrier density is tuned from $10^{17}$ to $10^{20}$ $cm^{-3}$ and identify two critical doping levels corresponding to the filling thresholds of the upper bands. At the first critical doping, which separates the single-band and the two-band superconducting regimes in oxygen-deficient samples, the steady increase of T$_{c}$ with carrier concentration suddenly stops. Near this doping level, the energy dispersion in the lowest band displays a downward deviation from parabolic behavior. The results impose new constraints for microscopic pairing scenarios. 
Xiao Lin, German Bridoux, Adrien Gourgout, Gabriel Seyfarth, Steffen   Kraemer, Marc Nardone, Benoit Fauque and Kamran Behnia
cond-mat.supr-con