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

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