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The average-density approximation is used to construct a nonlocal kineticenergy functional for an inhomogeneous two-dimensional Fermi gas. Thisfunctional is then used to formulate a Thomas-Fermi von Weizs\"acker-liketheory for the description of the ground state properties of the system. Thequality of the kinetic energy functional is tested by performing a fullyself-consistent calculation for an ideal, harmonically confined,two-dimensional system. Good agreement with exact results are found, with thenumber and kinetic energy densities exhibiting oscillatory structure associatedwith the nonlocality of the energy functional. Most importantly, thisfunctional shows a marked improvement over the two-dimensional Thomas-Fermi vonWeizs\"acker theory, particularly in the vicinity of the classically forbiddenregion.

A nonlocal kinetic energy functional for an inhomogeneous two-dimensional Fermi gas