Variation of the properties of a fully spin-polarized two-dimensional electron gas that is separated from its neutralizing background*

In most of the cases, one studies a two-dimensional electron gas (2DEG) system by assuming that the electrons are immersed in a jellium neutralizing positive background. The standard approach is to view the system of electrons confined on the same layer as the 2D jellium background. This well-known model has been very useful to explain various properties and possible quantum phase transitions that occur in such a 2D system. The objective of this work is to study the properties of a fully spin-polarized 2DEG model in the thermodynamic limit with the modification that the 2D system of electrons is separated by an arbitrary distance from the neutralizing 2D layer. We use a Hartree-Fock (HF) approach and find that the separation of the 2D system of electrons from the 2D jellium background acts as an effective kinetic energy that increases the overall energy of the system. This effective increase of kinetic energy by the separation effect is more pronounced at high density values where electronic liquid states are energetically more favored compared to Wigner solid states. This leads us to believe that the effect observed would adversely affect the energetic stability of the liquid electronic states in such a way as to further enhance the Wigner crystallization process.