The paper reports on the large electric-field response of quasi-two-dimensional (q2-DEG) electron gases generated at interfaces in epitaxial heterostructures made from insulating oxides. These structures, characterized by doping layers spatially separated from high-mobility q2-DEGs, mimic semiconducting high-electron mobility transistors. By applying gate voltages, the conductivity of the electron gases can be modulated through a quantum phase transition from insulating to metallic states. The q2-DEGs are formed at the interface between LaAlO3 and SrTiO3, with electron mobilities up to 10^6 cm^2 V^-1 s^-1. The thickness of LaAlO3 layers can be adjusted to control the conductivity, with critical thicknesses of 4 unit cells (uc) required for conductivity. Field-effect doping is achieved by altering the thickness of LaAlO3 layers, and the q2-DEGs exhibit pronounced memory effects. The study also explores the memory behavior of the q2-DEGs, which is influenced by the electronic properties of SrTiO3, potentially involving defect states and charge excitations. These findings open new avenues for designing oxide-based electronic devices.The paper reports on the large electric-field response of quasi-two-dimensional (q2-DEG) electron gases generated at interfaces in epitaxial heterostructures made from insulating oxides. These structures, characterized by doping layers spatially separated from high-mobility q2-DEGs, mimic semiconducting high-electron mobility transistors. By applying gate voltages, the conductivity of the electron gases can be modulated through a quantum phase transition from insulating to metallic states. The q2-DEGs are formed at the interface between LaAlO3 and SrTiO3, with electron mobilities up to 10^6 cm^2 V^-1 s^-1. The thickness of LaAlO3 layers can be adjusted to control the conductivity, with critical thicknesses of 4 unit cells (uc) required for conductivity. Field-effect doping is achieved by altering the thickness of LaAlO3 layers, and the q2-DEGs exhibit pronounced memory effects. The study also explores the memory behavior of the q2-DEGs, which is influenced by the electronic properties of SrTiO3, potentially involving defect states and charge excitations. These findings open new avenues for designing oxide-based electronic devices.