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

A novel nontrivial manifestation of quantum effects in a spherical mesoscopic system of degenerate electrons (with N e ≲ 10 9 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...

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Bibliographic Details
Published in:Physics Uspekhi 2021-10, Vol.64 (8), p.836-851
Main Authors: Kuratov, S E, Shidlovski, D S, Blinnikov, S I, Igashov, S Yu
Format: Article
Language:English
Subjects:
density-functional theory
Distribution functions
Electron distribution
electron distribution in a spherical potential
Electrons
Exact solutions
Green's functions
Green’s function
jellium model
Qualitative analysis
Spherical shells
Wave functions
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Summary:A novel nontrivial manifestation of quantum effects in a spherical mesoscopic system of degenerate electrons (with N e ≲ 10 9 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 infinitely deep 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.
ISSN:1063-7869
1468-4780
DOI:10.3367/UFNe.2020.08.038817