Nonlinear screening in two-dimensional electron gases

TL;DR

This paper investigates nonlinear screening in 2D electron gases using density functional theory, revealing bound states for a point charge Z=1 even at high densities, and proves the validity of linear response theory in this context.

Contribution

It introduces a self-consistent DFT approach to nonlinear screening and proves that linear response theory remains valid despite the existence of bound states.

Findings

Bound states exist for Z=1 charge even at high densities.

Linear response theory remains valid despite nonlinear effects.

Self-consistent calculations confirm theoretical predictions.

Abstract

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.