Effective Hamiltonians for Magnetic Ordering Within Periodic Anderson-Hubbard Model for Quantum Dot Array

  • L. Didukh
  • Yu. Skorenkyy
  • O. KramarEmail author
  • Yu. Dovhopyaty
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 221)


A generalized model of strongly correlated electron system in quantum dot arrays with magnetic impurity levels hybridized with conduction band is considered. The effective Hamiltonians on the basis of configurational representation with Hubbard X-operators describing the localized spin subsystem are developed for the regime of strong electron correlations. Comparison of indirect exchange integrals in single-particle energy spectrum give hints for understanding mechanisms of the magnetic ordering.


  1. 1.
    Chakraborty T (1999) Quantum dots: a survey of the properties of artificial atoms. Elsevier Science, AmsterdamCrossRefGoogle Scholar
  2. 2.
    Lan H, Ding Y (2012) Ordering, positioning and uniformity of quantum dot arrays. Nano Today 7:94–123CrossRefGoogle Scholar
  3. 3.
    Fesenko O, Yatsenko L (2018) Nanooptics, Nanophotonics, nanostructures, and their applications. NANO 2017. Springer proceedings in physics, vol. Springer, Cham, p 210Google Scholar
  4. 4.
    Anderson PW (1961) Localized magnetic states in metals. Phys Rev 124:41–53ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    Didukh LD, Stasyuk IV (1968) Effective Hamiltonian in the Anderson model. Fiz Met Metalov 26:582–588. [In Russian]Google Scholar
  6. 6.
    Didukh LD, Stasyuk IV [In Russian] (1968) On ferromagnetism theory with account of s-d transfer. Ukr Fiz Zhurn 13:1774–1780. In Russian]Google Scholar
  7. 7.
    Zhang P, Xue Q-K, Wang Y, Xie XC (2002) Spin-dependent transport through an interacting quantum dot. Phys Rev Lett 89:286803ADSCrossRefGoogle Scholar
  8. 8.
    Dias da Silva L, Ingersent K, Sandler N, Ulloa SE (2008) Finite-temperature conductance signatures of quantum criticality in double quantum dots. Phys Rev B 78:153304ADSCrossRefGoogle Scholar
  9. 9.
    Nikkarila J-P, Koskinen M, Manninen M (2008) Magnetism of quantum dot clusters: a Hubbard model study. Eur Phys J B 64:95–103ADSCrossRefGoogle Scholar
  10. 10.
    Hang Xie, Xiao Cheng, Xiaolong Lv (2018) Steady and dynamic magnetic phase transitions in interacting quantum dots arrays coupled with leads. Available via
  11. 11.
    Didukh L, Kramar O (2005) Metallic ferromagnetism in the systems with strongly correlated electrons. Condens Matter Phys 8:547–564CrossRefGoogle Scholar
  12. 12.
    Didukh L, Yu S, Kramar O (2008) Electron correlations in narrow energy bands: modified polar model approach. Condens Matter Phys 11:443–454CrossRefGoogle Scholar
  13. 13.
    Górski G, Mizia J, Kucab K (2015) Alternative equation of motion approach applied to transport through a quantum dot. Phys E 73:76–82CrossRefGoogle Scholar
  14. 14.
    Górski G, Mizia J, Kucab K (2016) Modified equation of motion approach for metallic ferromagnetic systems with the correlated hopping interaction. Phys Status Solidi B 253:1202–1209ADSCrossRefGoogle Scholar
  15. 15.
    Górski G, Kucab K (2018) Effect of assisted hopping on spin-dependent thermoelectric transport through correlated quantum dot. Phys B Condens Matter 545:337–345ADSCrossRefGoogle Scholar
  16. 16.
    Didukh L, Skorenkyy Y, Hankevych V, Kramar O (2001) Ground state ferromagnetism in a doubly orbitally degenerate model. Phys Rev B 64:144428ADSCrossRefGoogle Scholar
  17. 17.
    Didukh L, Kramar O, Skorenkyy Y (2002) Ground state energy of metallic ferromagnet in a generalized Hubbard model. Phys Status Solidi B 229:1241–1254ADSCrossRefGoogle Scholar
  18. 18.
    Didukh L, Kramar O (2002) Metallic ferromagnetism in a generalized Hubbard model. Fizika Nizkikh Temperatur (Kharkov) 28:42–50Google Scholar
  19. 19.
    Didukh L, Kramar O, Yu S (2005) Metallic ferromagnetism in a generalized Hubbard model. In: Murray VN (ed) New developments in ferromagnetism research. Nova Science Publishers Inc, New YorkGoogle Scholar
  20. 20.
    Skorenkyy Y, Didukh L, Kramar O, Dovhopyaty Y (2007) Mott transition, ferromagnetism and conductivity in the generalized Hubbard model. Acta Phys Pol A 111:635–644ADSCrossRefGoogle Scholar
  21. 21.
    Górski G, Mizia J, Kucab K (2014) New Green’s function approach describing the ferromagnetic state in the Hubbard model with correlated hopping. Phys Status Solidi B 251:2294–2301ADSCrossRefGoogle Scholar
  22. 22.
    Didukh L (2018) 3d-electrons contribution to cohesive energy of 3d-metals. Condensed Matter Physics 21:13701CrossRefGoogle Scholar
  23. 23.
    Izyumov YA, Kurmaev EZ (2008) Materials with strong electron correlations. Physics-Uspekhi 51:23ADSCrossRefGoogle Scholar
  24. 24.
    Shishido H et al (2010) Tuning the dimensionality of the heavy fermion compound CeIn3. Science 327:980–983ADSCrossRefGoogle Scholar
  25. 25.
    Zaitsev RO, Kuz’min EV, Ovchinnikov SG (1986) Fundamental ideas on metal-dielectric transitions in 3d-metal compounds. Sov Phys Usp 29:322–342ADSCrossRefGoogle Scholar
  26. 26.
    Fazekas P (1999) Lecture notes on electron correlation and magnetism. World Scientific Publishing, SingaporeCrossRefGoogle Scholar
  27. 27.
    Didukh L, Hankevych V, Kramar O, Skorenkyy Y (2002) Itinerant ferromagnetism of systems with orbital degeneracy. J Phys Condens Matter 14:827–835ADSCrossRefGoogle Scholar
  28. 28.
    Masuda S, Tan KY, Nakahara M (2018) Spin-selective electron transfer in quantum dot array. Phys Rev B 97:045418ADSCrossRefGoogle Scholar
  29. 29.
    Górski G, Mizia J (2009) Hubbard model with intersite kinetic correlations. Phys Rev B 83:064410ADSCrossRefGoogle Scholar
  30. 30.
    Skorenkyy Y, Kramar O, Didukh L, Dovhopyaty Y (2018) Electron correlation effects in theoretical model of doped fullerides. In: Fesenko O, Yatsenko L (eds) Nanooptics, nanophotonics, nanostructures, and their applications. NANO 2017. Springer proceedings in physics, vol 210. Springer, ChamGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • L. Didukh
    • 1
  • Yu. Skorenkyy
    • 1
  • O. Kramar
    • 1
    Email author
  • Yu. Dovhopyaty
    • 1
  1. 1.Ternopil Ivan Puluj National Technical UnіversityTernopilUkraine

Personalised recommendations