Limit of the electrostatic doping in two-dimensional electron gases of LaXO3(X = Al, Ti)/SrTiO3

In LaTiO₃/SrTiO₃ and LaAlO₃/SrTiO₃ heterostructures, the bending of the SrTiO₃ conduction band at the interface forms a quantum well that contains a superconducting two-dimensional electron gas (2-DEG). Its carrier density and electronic properties, such as superconductivity and Rashba spin-orbit coupling can be controlled by electrostatic gating. In this article we show that the Fermi energy lies intrinsically near the top of the quantum well. Beyond a filling threshold, electrons added by electrostatic gating escape from the well, hence limiting the possibility to reach a highly-doped regime. This leads to an irreversible doping regime where all the electronic properties of the 2-DEG, such as its resistivity and its superconducting transition temperature, saturate. The escape mechanism can be described by the simple analytical model we propose.