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 LaAlO_{3}/SrTiO_{3} 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.