Kinetic energy functional for a two-dimensional electron system

The noninteracting, nonuniform electron gas exhibits simplifications in two dimensions that are of particular interest in the application of density functional theory. The results of linear response theory for an attractive impurity in a two-dimensional gas have been shown to be surprisingly accurate even though there are bound states and are shown to be exact in the high density limit. We offer the alternative view that these results depend not so much on the properties of linear response but on a special feature of all density response functions in two dimensions. This feature leads to the result that all density gradient corrections to the Thomas-Fermi result for the electron kinetic energy functional vanish in two dimensions at zero temperature. This is not to say that the Thomas-Fermi result is exact, but numerical calculations show that it is a very good approximation for an attractive potential even in a low density gas.