Figure 1: (a) Lattice structure of the $\text{STO}$-$\text{LAO}$ interface, showing the unpoled $\text{SrO}$ and ${\text{TiO}}_2$ planes in $\text{STO}$ as well as the ${\text{LaO}}^{+}$ and ${\text{AlO}}_2^{-}$ planes with alternating polarity in $\text{LAO}$. (b) Simulation of the $\text{LAO}$ overlayer by an electrolytic gel with frozen-in polarization, allowing for controlled tuning of the charge-carrier density in the two-dimensional electron gas. The diagrams to the right of (a) and (b) show the potential energy of the $\text{LAO}$ overlayer and of the polarized gel, respectively, increasing linearly with layer thickness.