Carrier density and disorder are two crucial parameters that control the properties of correlated two-dimensional electron systems. In order to disentangle their individual contributions to quantum phenomena, independent tuning of these two parameters is required. Here, by utilizing a hybrid liquid/solid electric dual-gate geometry acting on the conducting LaAlO3/SrTiO3 heterointerface, we obtain an additional degree of freedom to strongly modify the electron confinement profile and thus the strength of interfacial scattering, independent from the carrier density. A dual-gate controlled nonlinear Hall effect is a direct manifestation of this profile, which can be quantitatively understood by a Poisson-Schrodinger subband model. In particular, the large nonlinear dielectric response of SrTiO3 enables a very wide range of tunable density and disorder, far beyond that for conventional semiconductors. Our study provides a broad framework for understanding various reported phenomena at the LaAlO3/SrTiO3 interface.
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