Nonlinear screening and stopping power in two-dimensional electron gases

TL;DR

This paper investigates nonlinear screening and stopping power in 2D electron gases using density functional theory, revealing significant nonlinear effects, the existence of bound states, and the validity of perturbation theory in high-density regimes.

Contribution

It provides a detailed analysis of nonlinear screening in 2D electron gases, deriving a high density screening theorem and challenging previous assumptions about perturbation theory validity.

Findings

Nonlinear screening significantly affects stopping power calculations.

Bound states exist in high-density 2D electron gases with nonlinear screening.

Perturbation theory remains valid even when bound states are supported.

Abstract

We have used density functional theory to study the nonlinear screening properties of a two-dimensional (2D) 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 behaviour 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.