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

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

2010-12-01

arxiv.org/abs/1012.0347v2

Physics

Condensed Matter

Quantum Gases

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

Scientific paper

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 Weizs\"acker-like gradient correction, which in the high-temperature limit, goes over to the familiar functional form $(\hbar^2/24m) (\nabla\rho)^2/\rho$. 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.

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