Simple exchange-correlation potential with a proper long-range behavior for low-dimensional nanostructures

TL;DR

This paper introduces a new exchange-correlation potential for two-dimensional systems that corrects the incorrect long-range decay present in common approximations, improving accuracy in low-dimensional nanostructures.

Contribution

It provides a simple, generalized-gradient approximation exchange-correlation potential with proper long-range behavior specifically designed for two-dimensional systems.

Findings

The corrected potential matches the analytic two-electron quantum dot results asymptotically.

It produces plausible exchange-correlation potentials for larger 2D systems.

The potential is as easy to apply as the local-density approximation.

Abstract

The exchange-correlation potentials stemming from the local-density approximation and several generalized-gradient approximations are known to have incorrect asymptotic decay. This failure is independent of the dimensionality, but so far the problem has been corrected -- within the mentioned approximations -- only in three dimensions. Here we provide a cured exchange-correlation potential in two dimensions, where the applications have a continuously increasing range in, e.g., semiconductor physics. The given potential is a generalized-gradient approximation, which is as easy to apply as the local-density approximation. We demonstrate that the corrected potential agrees very well with the analytic result of a two-electron quantum dot in the asymptotic regime, and yields plausible exchange-correlation potentials for larger two-dimensional systems.