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

S.E. Kuratov^†^a, D.S. Shidlovski^a, b, S.I. Blinnikov^a, b, S.Yu. Igashov^a
^aDukhov Research Institute of Automatics, ul. Sushchevskaya 22, Moscow, 119017, Russian Federation
^bNational 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 N_e ≲ 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.

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
URL: https://ufn.ru/en/articles/2021/8/e/
Web of Science

000711503200009
Scopus

2-s2.0-85119689311
ADS NASA

2021PhyU...64..836K
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. 64 836–851 (2021)

BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Received: 8th, July 2020, accepted: 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

References (37) ↓ Cited by (2) Similar articles (14)

Kirzhnits D A, Lozovik Yu E, Shpatakovskaya G V Usp. Fiz. Nauk 117 3 (1975); Kirzhnits D A, Lozovik Yu E, Shpatakovskaya G V Sov. Phys. Usp. 18 649 (1975)
Shpatakovskaya G V Usp. Fiz. Nauk 182 457 (2012); Shpatakovskaya G V Phys. Usp. 55 429 (2012)
Shpatakovskaya G V Zh. Eksp. Teor. Fiz. 125 518 (2004); Shpatakovskaya G V J. Exp. Theor. Phys. 98 455 (2004)
Kirzhnits D A, Shpatakovskaya G V Zh. Eksp. Teor. Fiz. 62 2082 (1972); Kirzhnits D A, Shpatakovskaya G V Sov. Phys. JETP 35 1088 (1972)
Ekardt W Phys. Rev. B 29 1558 (1984)
Gamow G Nature 131 433 (1933)
Flügge S Practical Quantum Mechanics (New York: Springer-Verlag, 1971); Per. na russk. yaz., Flyugge Z Zadachi Po Kvantovoi Mekhanike (M.: Nauka, 1974)
Messiah A Quantum Mechanics Vol. 1 (Amsterdam: North-Holland Publ. Co., 1961); Per. na russk. yaz., Messia A Kvantovaya Mekhanika Vol. 1 (M.: Nauka, 1979)
Varshalovich D A, Moskalev A N, Khersonskii V K Kvantovaya Teoriya Uglovogo Momenta (L.: Nauka, 1975); Per. na angl. yaz., Varshalovich D A, Moskalev A N, Khersonskii V K Quantum Theory Of Angular Momentum (Singapore: World Scientific Publ., 1988)
Abramowitz M, Stegun I A (Eds) Handbook Of Mathematical Functions With Formulas, Graphs, And Mathematical Tables (New York: Dover Publ., 1972); Per. na russk. yaz., Abramovits M, Stigan I (Red.) Spravochnik Po Spetsial’nym Funktsiyam s Formulami, Grafikami i Matematicheskimi Tablitsami (M.: Nauka, 1979)
Prudnikov A P, Brychkov Yu A, Marichev O I Integraly i Ryady T. 2 Spetsial’nye Funktsii (M.: Nauka, 2003)
Baz’ A I, Zel’dovich Ya B, Perelomov A P Rasseyanie, Reaktsii i Raspady v Nerelyativistskoi Kvantovoi Mekhanike (M.: Nauka, 1971)
Amos D E ACM Trans. Math. Software 12 265 (1986)
Bremer J arXiv:1705.07820
Strutinskii V M, Magner A G Fiz. Elem. Chast. At. Yad. 7 356 (1976); Strutinskii V M, Magner A G Sov. J. Part. Nucl. 7 138 (1976)
Gutzwiller M C J. Math. Phys. 8 1979 (1967)
Gutzwiller M C J. Math. Phys. 10 1004 (1969)
Gutzwiller M C J. Math. Phys. 11 1791 (1970)
Reichl L E The Transition To Chaos: Conservative Classical Systems And Quantum Manifestations (New York: Springer, 2004)
Koch E, Gunnarsson O Phys. Rev. B 54 5168 (1996)
Perdew J P, Tran H Q, Smith E D Phys. Rev. B 42 11627 (1990)
Perdew J P Prog. Surf. Sci. 48 245 (1995)
Kiejna A Prog. Surf. Sci. 61 85 (1999)
Kohn W, Sham L J Phys. Rev. 140 A1133 (1965)
Perdew J P, Zunger A Phys. Rev. B 23 5048 (1981)
Shidlovski D S, Mukhanov A E J. Phys. Conf. Ser. 1009 012012 (2018)
Puska M, Ogando E, Zabala N Phys. Rev. B 64 033401 (2001)
Elsasser W M J. Phys. Radium 4 549 (1933)
Kuratov S E, Shidlovski D S, Blinnikov S I Phys. Plasmas 26 022709 (2019)
Kim J-H et al Phys. Rev. E 96 042205 (2017)
Datta S Electronic Transport In Mesoscopic Systems (Cambridge: Cambridge Univ. Press, 1995)
Li Y et al Nanoscale Res. Lett. 10 420 (2015)
Sun J P et al Proc. IEEE 86 641 (1998)
Capri A Z Problems And Solutions In Nonrelativistic Quantum Mechanics (River Edge, NJ: World Scientific, 2002)
Friedel J Philos. Mag. 43 153 (1952)
Kohn W, Vosko S H Phys. Rev. 119 912 (1960)
Whittaker E T, Watson G N A Course Of Modern Analysis (Cambridge: The Univ. Press, 1927); Per. na russk. yaz., Uitteker E T, Vatson Dzh N Kurs Sovremennogo Analiza Ch. 1 Osnovnye Operatsii Analiza (M.: Fizmatlit, 1962)