The two-dimensional homogeneous electron gas with symmetric dual-gate screening: exchange-correlation functional and other ground-state properties

TL;DR

This paper develops an accurate exchange-correlation functional for the 2D homogeneous electron gas with symmetric dual-gate screening, enabling improved density-functional calculations for experimental 2D systems with gate effects.

Contribution

It introduces a new correlation energy functional based on diffusion Monte Carlo data for 2D HEG with gate screening, enhancing theoretical modeling of realistic 2D materials.

Findings

Correlation energy fitted across densities and gate separations

Gate screening significantly alters bulk modulus and pair correlations

Functional applicable to experimental 2D electron systems

Abstract

The two-dimensional (2D) homogeneous electron gas (HEG) is a fundamental model in quantum many-body physics. It is important to theoretical and computational studies, where exchange-correlation energies computed in it serve as the foundation for density-functional calculations. It is also of direct relevance to a variety of experimental settings, especially with the rapid recent growth in 2D materials and moir\'e systems. In these experiments, metallic gates are often present, which screen the Coulomb interaction between electrons. The effect of the screening can qualitatively change the behavior of the 2D HEG, and requires accurate many-body computations to capture. In this work, we perform state-of-the-art diffusion Monte Carlo (DMC) calculations in the 2D HEG subjected to symmetric dual-gate screening. We systematically compute the correlation energy across a range of densities and gate separations for both spin unpolarized and fully polarized systems. A global fit is obtained for the correlation energy, using these data and imposing various limiting behaviors obtained from perturbation analysis. The new functional will allow density-functional calculations to be performed for a variety of realistic experimental setups which can accurately account for the presence of gates. We also investigate how the gate screening affects the bulk modulus, pair correlation function, and the structure factor of the 2D HEG, which can potentially be probed in experiments.