Two-dimensional limit of exchange-correlation energy functional approximations in density functional theory

TL;DR

This paper reveals fundamental limitations of common 3D exchange-correlation functionals in density functional theory when applied to 2D systems, highlighting the superiority of nonlocal functionals like ADA for such cases.

Contribution

The study demonstrates the failure of LDA, GGA, and MGGA in the strong 2D limit and shows that nonlocal functionals like ADA are more accurate for 2D systems.

Findings

LDA, GGA, MGGA perform worse than LDA in the 2D limit

Nonlocal functionals like ADA are highly accurate for quasi-2D systems

Implications for practical device simulations and material studies

Abstract

We investigate the behavior of three-dimensional (3D) exchange-correlation energy functional approximations of density functional theory in anisotropic systems with two-dimensional (2D) character. Using two simple models, quasi-2D electron gas and two-electron quantum dot, we show a {\it fundamental limitation} of the local density approximation (LDA), and its semi-local extensions, generalized gradient approximation (GGA) and meta-GGA (MGGA), the most widely used forms of which are worse than the LDA in the strong 2D limit. The origin of these shortcomings is in the inability of the local (LDA) and semi-local (GGA/MGGA) approximations to describe systems with 2D character in which the nature of the exchange-correlation hole is very nonlocal. Nonlocal functionals provide an alternative approach, and explicitly the average density approximation (ADA) is shown to be remarkably accurate for the quasi-2D electron gas system. Our study is not only relevant for understanding of the functionals but also practical applications to semiconductor quantum structures and materials such as graphite and metal surfaces. We also comment on the implication of our findings to the practical device simulations based on the (semi-)local density functional method.