Airy-averaged gradient corrections for two-dimensional fermion gases

Abstract

Building on the discussion in PRA 93, 042510 (2016), we present a systematic derivation of gradient corrections to the kinetic-energy functional and the one-particle density, in particular for two-dimensional systems. We derive the leading gradient corrections from a semiclassical expansion based on Wigner's phase space formalism and demonstrate that the semiclassical kinetic-energy density functional at zero temperature cannot be evaluated unambiguously. In contrast, a density-potential functional description that effectively incorporates interactions provides unambiguous gradient corrections. Employing an averaging procedure that involves Airy functions, thereby partially resumming higher-order gradient corrections, we facilitate a smooth transition of the particle density into the classically forbidden region of arbitrary smooth potentials. We find excellent agreement of the semiclassical Airy-averaged particle densities with the exact densities for very low but finite temperatures, illustrated for a Fermi gas with harmonic potential energy. We furthermore provide criteria for the applicability of the semiclassical expansions at low temperatures. Finally, we derive a well-behaved ground-state kinetic-energy functional, which improves on the Thomas-Fermi approximation.

24 pages, 8 figures. Changes to version 1: layout modified, footnotes 1 & 12 added, one paragraph added on page 7

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Cited by in corpus (6)

• Universal Functionals in Density Functional Theory
• Systematic corrections to the Thomas-Fermi approximation without a gradient expansion
• First-principles quantum corrections for carrier correlations in double-layer two-dimensional heterostructures
• Self-consistent assessment of Englert-Schwinger model on atomic properties
• Single-particle-exact density functional theory
• Phase Transitions of Repulsive Two-Component Fermi Gases in Two Dimensions