Anomalous Frequency and Temperature Dependent Scattering in the Dilute Metallic Phase in Lightly Doped SrTiO_{3}

The mechanism of superconductivity in materials with aborted ferroelectricity and its emergence out of a dilute metallic phase in systems like doped SrTiO_{3} is an outstanding issue in condensed matter physics. This dilute metal has anomalous properties that are both similar and different to those found in the normal state of other unconventional superconductors. For instance, T^{2} resistivity can be found at densities that are too small to allow current decay through electron-electron scattering. We have investigated the optical properties of the dilute metallic phase in doped SrTiO_{3} using THz time-domain spectroscopy. At low frequencies the THz response exhibits a Drude-like form as expected for typical metal-like conductivity. We observed the frequency and temperature dependencies to the low energy scattering rate Γ(ω,T)∝(ℏω)^{2}+(pπk_{B}T)^{2} expected in a conventional Fermi liquid. However, we find the lowest known p values of 0.39-0.72. As p is 2 in a canonical Fermi liquid and existing models based on energy dependent elastic scattering bound p from below to 1, our observation lies outside current explanation. Our data also give insight into the high temperature regime and show that the temperature dependence of the resistivity derives in part from strong T dependent mass renormalizations.