Pseudo-proper two-dimensional electron gas formation

In spite of the interest in the two-dimensional electron gases (2DEGs) experimentally found at surfaces and interfaces, important uncertainties remain about the observed insulator–metal transitions (IMTs). Here we show how an explicit improper coupling of carrier sources with a relevant soft mode significantly affects the transition. The analysis presented here for 2DEGs at polar interfaces is based on group theory, Landau-Ginzburg theory, and illustrated with first-principles calculations for the prototypical case of the LaAlO${}_3$/SrTiO${}_3$ interface, for which such a structural transition has recently been observed. This direct coupling implies that the appearance of the soft mode is always accompanied by carriers. For sufficiently strong coupling an avalanche-like first-order IMT is predicted.