A simple variational method for calculating energy and quantum capacitance of an electron gas with screened interactions

TL;DR

This paper introduces a variational method to compute the energy and quantum capacitance of an electron gas with screened Coulomb interactions, validated against Monte Carlo data and experimental results.

Contribution

The paper presents a simple variational approach for calculating properties of an electron gas with screened interactions, offering an efficient alternative to complex simulations.

Findings

The variational method accurately predicts the energy of the electron gas.

Quantum capacitance results agree with experimental data.

Method shows good agreement with Monte Carlo simulations.

Abstract

We describe a variational procedure for calculating the energy of an electron gas in which the long-range Coulomb interaction is truncated by the screening effect of a nearby metallic gate. We use this procedure to compute the quantum capacitance of the system as a function of electron density and spin polarization. The accuracy of the method is verified against published Monte-Carlo data. The results compare favorably with a recent experiment.