Interaction of fast charged projectiles with two-dimensional electron gas: Interaction and disorder effects

TL;DR

This paper presents a theoretical study of how ions lose energy when moving through a disordered two-dimensional electron gas, considering damping effects, and explores the validity of the equipartition sum rule in two dimensions.

Contribution

It introduces a generalized equipartition sum rule for 2D electron gases and analyzes the impact of damping and interactions on stopping power calculations.

Findings

Damping reduces the stopping power at various velocities.

The equipartition sum rule does not always hold in 2D systems.

New results on exchange-correlation effects in 2D electron gases.

Abstract

The results of a theoretical investigation on the stopping power of ions moving in a disordered two-dimensional degenerate electron gas are presented. The stopping power for an ion is calculated employing linear response theory using the dielectric function approach. The disorder, which leads to a damping of plasmons and quasiparticles in the electron gas, is taken into account through a relaxation time approximation in the linear response function. The stopping power for an ion is calculated in both the low- and high-velocity limits. In order to highlight the effects of damping we present a comparison of our analytical and numerical results, in the case of point-like ions, obtained for a non-zero damping with those for a vanishing damping. It is shown that the equipartition sum rule first formulated by Lindhard and Winther for three-dimensional degenerate electron gas does not necessarily hold in two-dimensions. We have generalized this rule introducing an effective dielectric function. In addition some new results for two-dimensional interacting electron gas have been obtained. In this case the exchange-correlation interactions of electrons are considered via local-field-corrected dielectric function.