We report on superconductivity in single crystals of SrTiO$_{ 3-\delta}$ with carrier densities $\textit{ n} < 1.4 \times10^{ 18}cm^{ -3}$, where only a single band is occupied. For all samples in this regime, the resistive transition occurs at $T_{ c} \approx 65 \pm 25 \ mK$. We observe a zero resistance state for $\textit{ n}$ as low as $1.03 \times10^{ 17}cm^{ -3}$, and a partial resistive transition for $\textit{ n} = 3.85 \times10^{ 16}cm^{ -3}$. We observe low critical current densities, relatively high and isotropic upper critical fields, and an absence of diamagnetic screening in these samples. Our findings suggest an inhomogeneous superconducting state, embedded within a homogeneous high-mobility 3-dimensional electron gas. $T_{ c}$ does not vary appreciably when $\textit{ n}$ changes by more than an order of magnitude, inconsistent with conventional superconductivity.
Categories: cond-mat.supr-con