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

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.