Generalization of the Thomas — Fermi theory for the two-dimensional electron gas

Authors: Terebizh A.A.
Published in issue: #5(82)/2023
DOI: 10.18698/2541-8009-2023-5-897
Category: Physics | Chapter: Physics and technology of nanostructures, nuclear and molecular
Keywords: density functional method, generalized gradient expansion, gradient corrections, Kirzhnitz method, Thomas — Fermi theory, electron density, two-dimensional electron gas, kinetic energy functional
Published: 22.05.2023

The paper presents generalization of the classical expression of the Thomas — Fermi theory for the case of the two-dimensional electron gas. The effect of electron density gradients responsible for inhomogeneities in real systems was considered within the framework of the generalized gradient expansion. Derivation of the electron density approximation through the function expansion in terms on commutators of the operators of the coordinate and momentum physical values is shown. Relationship between the system chemical potential and the external field was taken into account. A differential equation was obtained necessary to determine characteristics of the system, which explicitly depended on the space dimension. To substantiate correctness of the results for the two-dimensional case, widely known results for the three-dimensional case were obtained from the derived D-dimensional equation. Kinetic energy functional was constructed that depended on the electron density and described behavior of the inhomogeneous two-dimensional electron cloud.

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