Nonlinear screening in two-dimensional electron gases

We have performed self-consistent calculations of the nonlinear screening of a point charge Z in a two-dimensional electron gas using a density functional theory method. We find that the screened potential for a Z=1 charge supports a bound state even in the high density limit where one might expect perturbation theory to apply. To explain this behaviour, we prove a theorem to show that the results of linear response theory are in fact correct even though bound states exist.