Nonlinear screening and stopping power in two-dimensional electron gases

We have used density-functional theory to study the nonlinear screening properties of a two-dimensional s2Dd electron gas. In particular, we consider the screening of an external static point charge of magnitude Z as a function of the distance of the charge from the plane of the gas. The self-consistent screening potentials are then used to determine the 2D stopping power in the low-velocity limit based on the momentum transfer cross section. Calculations as a function of Z establish the limits of validity of linear and quadratic response theory calculations, and show that nonlinear screening theory already provides significant corrections in the case of protons. In contrast to the 3D situation, we find that the nonlinearly screened potential supports a bound state even in the high-density limit. This behavior is elucidated with the derivation of a high-density screening theorem which proves that the screening charge can be calculated perturbatively in the high-density limit for arbitrary dimensions. However, the theorem has particularly interesting implications in 2D where, contrary to expectations, we find that perturbation theory remains valid even when the perturbing potential supports bound states.