Jellium model of the two-dimensional Airy electron gas at the perovskite titanate interface

We describe the observed charge modulation at the recently fabricated perovskite titanate trilayer interface (SrTiO3)(m)/(LaTiO3)(1)/(SrTiO3)(m) in terms of a two-dimensional Airy electron gas within the jellium model. The positively charged La layer is described as a uniformly charged sheet, which produces a uniform electric field via Gauss's law, in which the stripped-off electrons from the La atoms become confined, producing a two-dimensional Airy gas. We describe this gas in the local density approximation to the density functional theory. The electron gas spreads to several layers on either side of the interface, decaying exponentially into the SrTiO3 bulk region, consistent with the Ti3+ fraction observed in the electron-energy-loss spectroscopy experiments as well as with the results of the more involved ab initio density-functional calculations.