AbstractWe show here a new phenomenon in La_0.5Sr_0.5TiO₃/SrTiO₃ (LSTO/STO) heterostructures; that is a coexistence of three-dimensional electron liquid (3DEL) and 2D electron gas (2DEG), separated by an intervening insulating LSTO layer. The two types of carriers were revealed through multi-channel analysis of the evolution of nonlinear Hall effect as a function of film thickness, temperature and back gate voltage. We demonstrate that the 3D electron originates from La doping in LSTO film and the 2D electron at the surface of STO is due to the polar field in the intervening insulating layer. As the film thickness is reduced below a critical thickness of 6 unit cells (uc), an abrupt metal-to-insulator transition (MIT) occurs without an intermediate semiconducting state. The properties of the LSTO layer grown on different substrates suggest that the insulating phase of the intervening layer is a result of interface strain induced by the lattice mismatch between the film and substrate. Further, by fitting the magnetoresistance (MR) curves, the 6 unit cell thick LSTO is shown to exhibit spin-orbital coupling. These observations point to new functionalities, in addition to magnetism and superconductivity in STO-based systems, which could be exploited in a multifunctional context.