Capacitive probing of electronic phase separation in an oxide two-dimensional electron system

Interfaces between specific complex oxides host two-dimensional electron systems (2DESs) with strong electron-electron interactions. This combination yields a rich phenomenology, including an apparently intrinsic electronic phase separation (EPS). We designed an experiment to study the origins and magnitude of EPS in oxide 2DESs in more detail. We measure the capacitance between the 2DES at the LaAlO3/SrTiO3 interface and an electrode on top of the LaAlO3 as a function of applied gate voltage. Our measurements reveal a significant reduction of this capacitance in the region of the phase diagram where the charge-carrier density is low. The tunnel conductance is reduced as well, which implies that part of the interface becomes insulating. These measurements allow us to directly estimate the magnitude of the EPS at a carrier density of several 1013cm-2, higher than the nominal carrier density in most experiments. The pattern in the capacitance-voltage measurements reflecting the local metal-insulator transitions suggests that the main driver for EPS is a strong variation of the electrostatic potential with a non-normal probability distribution. We study the effect of this in-plane potential variation on the electronic properties of the 2DES by mapping the full superconducting dome as a function of both backgate and topgate voltage. This map shows that, once insulating patches emerge, the global critical temperature Tc falls, while the onset temperature - i.e., highest local Tc - remains fairly constant.