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 behavior, we prove a theorem to show that the results of linear response theory are in fact correct even though bound states exist.

Figure 1

Comparison of nonlinear and linear screened potentials: nonlinear with exchange correlation (solid), nonlinear Hartree potential (short-dashed), linear Hartree potential with LFC (chain); $Z=-1$, $r_s=4$.

Figure 2

Bound state eigenvalue vs $r_s$: nonlinear DFT with (solid) and without (dashed) exchange correlation.

Figure 3

Screening charge density for a model potential: bound (dashed) and continuum (chain) state contributions, total (solid). (a) $V_0=0.125\mathrm{H}$, (b) $V_0=0.25\mathrm{H}$; $r_s=0.5$.

Figure 4

Normalized stopping power as a function of the projectile charge $Z$, for $r_s=2$: nonlinear screening with (solid) and without (dashed) exchange correlation. The straight chain curve gives the quadratic response result.