Electric Field Tuned Crossover From Semi-Classical to Weakly Localized Quantum Transport in a Quasi 2-Dimensional Electron Gas in SrTiO$_3$*

Quasi 2-dimensional electron gases (Q2DEG) created by doping SrTiO$_3$ (STO) near interfaces and surfaces, have attracted considerable attention. These oxide Q2DEG's potentially offer a wide range of tunable behavior due to the extraordinary properties of STO. Here, we present electric field tuned magnetotransport measurements of a Q2DEG created by Ar- irradiation. The electric field, applied through a back gate bias, modulates both the mobility and sheet density, with a greater effect on the former. For high mobilities, the magnetotransport obeys Kohler's rule, consistent with semi- classical transport. As the mobility is decreased, violation of Kohler's rule is observed and weakly localized quantum transport emerges. This electric field tuned crossover arises from a modulation in the carrier confinement, which is enhanced by the electric field dependent dielectric constant of STO, as shown through self-consistent solutions to the Poisson and Schr\"odinger equations. The implications of our results on the development of oxide electronic devices will be discussed.