Energy of a Spin-Unpolarised Two-Dimensional Electron Gas Separated From a Neutralising Layer

We study a system of electrons forming a spin-unpolarised two-dimensional electron gas suspended over a neutralising jellium background layer. While a spin-unpolarised two-dimensional electron gas system represents the theoretical ground state in absence of interactions, we employ an anti-symmetrized Slater determinant wave function of plane waves to investigate the system when interactions are introduced. We analyse the dependence of the total energy on the density of the system and the separation between the two-dimensional electron gas and its neutralising layer. Our findings reveal that this layer separation introduces an added energy contribution that effectively behaves like a kinetic energy term. Consequently, the total energy of the electron liquid state increases with growing separation, an effect that becomes significantly more pronounced in the high-density regime.