Gradient corrections to the kinetic energy density functional of a two-dimensional Fermi gas at finite temperature

Abstract

We examine the leading order semiclassical gradient corrections to the non-interacting kinetic energy density functional of a two dimensional Fermi gas by applying the extended Thomas-Fermi theory at finite temperature. We find a non-zero von Weizsäcker-like gradient correction, which in the high-temperature limit, goes over to the familiar functional form $({\hslash }^2/24m)(\nabla \rho {)}^2/\rho$. Our work provides a theoretical justification for the inclusion of gradient corrections in applications of density-functional theory to inhomogeneous two-dimensional Fermi systems at any {\em finite} temperature.

14 pages, 2 Tables, 3 figures. Figs. 1 and 2 are colour. Accepted for publication in Physical Review B

References in corpus (2)

• T>0 ensemble state density functional theory revisited
• Kirzhnits gradient expansion for a D-dimensional Fermi gas

Cited by in corpus (6)

• Gradient correction and Bohm potential for 2D and 1D electron gases at a finite temperature
• On the Kirzhnits gradient expansion in two dimensions
• Airy-averaged gradient corrections for two-dimensional fermion gases
• A nonlocal kinetic energy functional for an inhomogeneous two-dimensional Fermi gas
• Evaluation of inverse integral transforms for undergraduate physics students
• Preserving the Hermiticity of the One-Body Density Matrix for a Non-Interacting Fermi Gas