Electric field effect near the metal-insulator transition of a two-dimensional electron system in SrTiO$_{\mathbf{3}}$

We report on the effects of electric field on the two-dimensional electron gas at the SmTiO$_{3}$/SrTiO$_{3}$ interface. Reducing the thickness of the SmTiO$_{3}$ depletes a significant fraction of the two-dimensional electron gas and drives it into the vicinity of a temperature-triggered metal insulator transition (257 K). After gate metal deposition, the sheet resistance exceeds the quantum resistance, $h$/e$^{2}$, and the SrTiO$_{3}$ channel is in the hopping regime at zero gate bias. We show that electric field effect can be used to tune the two-dimensional electron system in SrTiO$_{3}$ that is deep in the insulating phase ($R_{s}$ \textgreater 380 k$\Omega $/$\mathqed )$ to near the transition to a metal, which occurs at the quantum limit, $R_{s}$ \textasciitilde $h$/e$^{2}$. Saturation current densities and sheet resistance modulation cannot solely be explained by carrier density modulation, which was independently confirmed using capacitance-voltage measurements, indicating a change in the nature of transport as a function of electric field. The channel resistances as a function of temperature can all be scaled by a single parameter, which depends on the gate bias, similar to two-dimensional electron systems in high-quality semiconductors.