Methodological notes

Two scales of quantum effects in a mesoscopic system of degenerate electrons

  a,  a, b,  a, b,  a
a Dukhov Research Institute of Automatics, ul. Sushchevskaya 22, Moscow, 119017, Russian Federation
b National Research Center "Kurchatov Institute", Alikhanov Institute of Theoretical and Experimental Physics, ul. B. Cheremushkinskaya 25, Moscow, 117218, Russian Federation

A new nontrivial manifestation of quantum effects in a spherical mesoscopic system of degenerate electrons (with Ne ≲ 109 electrons) is demonstrated. Analysis shows that the electron distribution function has a large spatial scale, of the order of the system size, which is much greater than the other spatial scale, the Fermi length of the electron. This result is obtained following four different strategies: an analytic method of semiclassical Green's functions, direct numerical summation of the exact solutions for electron wave functions in an infinite potential well, numerical construction of the exact Green's function using two linearly independent solutions, and the density functional method. The results obtained with these methods are in good qualitative and quantitative agreement with each other. We relate the nature of this phenomenon to quantum shell effects in a spherical mesoscopic system.

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Keywords: electron distribution in a spherical potential, Green's function, density-functional theory, jellium model
PACS: 31.15.E−, 71.10.Ca, 71.15.Mb, 73.20.−r (all)
DOI: 10.3367/UFNe.2020.08.038817
Citation: Kuratov S E, Shidlovski D S, Blinnikov S I, Igashov S Yu "Two scales of quantum effects in a mesoscopic system of degenerate electrons" Phys. Usp. 64 (8) (2021)

Received: 8th, July 2020, 11th, August 2020

Оригинал: Куратов С Е, Шидловский Д С, Блинников С И, Игашов С Ю «Два масштаба квантовых эффектов в мезоскопической системе вырожденных электронов» УФН 191 882–898 (2021); DOI: 10.3367/UFNr.2020.08.038817

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