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

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.