Energy of a Fully Spin-Polarized Two-Dimensional Electron Gas Separated from its Jellium Neutralizing Background

We study a two-dimensional electron gas in which the electrons are separated from the corresponding jellium neturalizing background. For simplicity, we assume that the electrons are fully spin-polarized meaning that they are treated as spinless particles. The current setup implies that the overall energy of the system will depend on both density and separation distance of the electrons from the neutralizing background. The subtle interplay of these two parameters determines the stability of the system. Analytical results for the energy are obtained in the thermodynamic limit by using the Hartree-Fock approach. It is found that, within the framework of this approximation, the effect of separation manifests as an effective increase of kinetic energy.