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 $({\hslash }^2/24m)(\nabla \ddot{I}{)}^2/\ddot{I}$. 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