Correlation energy of two-dimensional systems: Toward non-empirical and universal modeling

TL;DR

This paper extends a successful 3D correlation energy approximation to 2D systems, enabling more accurate density-functional theory modeling of strongly correlated low-dimensional materials.

Contribution

It introduces a non-empirical, universal correlation energy functional for 2D systems that accounts for electron current and spin, improving accuracy over previous models.

Findings

Good agreement with exact data for quantum dots under magnetic fields

Accurate modeling of the 2D homogeneous electron gas

Enhanced non-empirical correlation functional for 2D systems

Abstract

The capability of density-functional theory to deal with the ground-state of strongly correlated low-dimensional systems, such as semiconductor quantum dots, depends on the accuracy of functionals developed for the exchange and correlation energies. Here we extend a successful approximation for the correlation energy of the three dimensional inhomogeneous electron gas, originally introduced by Becke [J. Chem. Phys. {\bf 88}, 1053 (1988)], to the two-dimensional case. The approach aims to non-empirical modeling of the correlation-hole functions satisfying a set of exact properties. Furthermore, the electron current and spin are explicitly taken into account. As a result, good performance is obtained in comparison with numerically exact data for quantum dots with varying external magnetic field, and for the homogeneous two-dimensional electron gas, respectively.