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

TL;DR

This paper derives and justifies the leading semiclassical gradient correction to the kinetic energy functional for a two-dimensional Fermi gas at finite temperature, enhancing the accuracy of density-functional theory in such systems.

Contribution

It provides the first theoretical derivation of a non-zero gradient correction for 2D Fermi gases at finite temperature, extending the extended Thomas-Fermi theory.

Findings

Gradient correction is non-zero and resembles von Weizsäcker form at high temperature.

The correction is valid for inhomogeneous 2D Fermi systems at finite temperature.

Provides theoretical basis for improved density-functional calculations.

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 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.