Single-gap superconductivity and dome of superfluid density in Nb-doped SrTiO3

Abstract: SrTiO$3$ exhibits a superconducting dome upon doping with Nb, with a maximum critical temperature \mbox{$T\mathrm{c} \approx 0.4$~K}. Using microwave stripline resonators at frequencies from 2 to 23~GHz and temperatures down to 0.02~K, we probe the low-energy optical response of superconducting SrTiO$3$ with charge carrier concentration from 0.3 to $2.2\times 10^{20}$~cm$^{-3}$, covering the majority of the superconducting dome. We find single-gap electrodynamics even though several electronic bands are superconducting. This is explained by a single energy gap $2\Delta$ due to gap homogenization over the Fermi surface consistent with the low level of defect scattering in Nb-doped SrTiO$_3$. Furthermore, we determine $T\mathrm{c}$, $2\Delta$, and the superfluid density as a function of charge carrier concentration, and all three quantities exhibit the characteristic dome shape.