Gaussian approximations for the exchange-energy functional of current-carrying states: Applications to two-dimensional systems

TL;DR

This paper develops simple, efficient exchange energy approximations for two-dimensional electronic systems, emphasizing the importance of gauge invariance for accurately describing current-carrying states within density-functional theory.

Contribution

It introduces new exchange energy functionals based on the short-range behavior of the one-body spin-density matrix, tailored for 2D systems with current-carrying states.

Findings

Accurate exchange energy approximations for 2D systems

Validation of gauge-invariance in current-carrying states

Excellent performance demonstrated in multiple applications

Abstract

Electronic structure calculations are routinely carried out within the framework of density-functional theory, often with great success. For electrons in reduced dimensions, however, there is still a need for better approximations to the exchange-correlation energy functional. Furthermore, the need for properly describing current-carrying states represents an additional challenge for the development of approximate functionals. In order to make progress along these directions, we show that simple and efficient expressions for the exchange energy can be obtained by considering the short-range behavior of the one-body spin-density matrix. Applications to several two-dimensional systems confirm the excellent performance of the derived approximations, and verify the gauge-invariance requirement to be of great importance for dealing with current-carrying states.