Quantum Nature of Two-Dimensional Electron Gas Confinement at LaAlO₃/SrTiO₃ Interfaces

We perform density functional calculations to understand the mechanism controlling the confinement width of the two-dimensional electron gas (2DEG) at LaAlO₃/SrTiO₃ interfaces. We find that the 2DEG confinement can be explained by the formation of metal induced gap states (MIGS) in the band gap of SrTiO₃. These states are formed as the result of quantum-mechanical tunneling of the charge created at the interface due to electronic reconstruction. The attenuation length of the MIGS into the insulator is controlled by the lowest-decay-rate evanescent states of SrTiO₃, as determined by its complex band structure. Our calculations predict that the 2DEG is confined in SrTiO₃ within about 1 nm at the interface.