  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.
