Spin-Dependent Transport of Carbon Nanotubes with Chromium Atoms

  • S. P. Kruchinin
  • S. P. RepetskyEmail author
  • I. G. Vyshyvana
Conference paper
Part of the NATO Science for Peace and Security Series A: Chemistry and Biology book series (NAPSA)


This paper presents a new method of describing electronic correlations in disordered magnetic crystals based on the Hamiltonian of multi-electron system and diagram method for Green’s functions finding. Electronic states of a system were approximately described by self-consistent multi-band tight-binding model. The Hamiltonian of a system is defined on the basis of Kohn–Sham orbitals. Potentials of neutral atoms are defined by the meta-generalized gradient approximation (MGGA). Electrons scattering on the oscillations of the crystal lattice are taken into account. The proposed method includes long-range Coulomb interaction of electrons at different sites of the lattice. Precise expressions for Green’s functions, thermodynamic potential and conductivity tensor are derived using diagram method. Cluster expansion is obtained for density of states, free energy, and electrical conductivity of disordered systems. We show that contribution of the electron scattering processes to cluster expansion is decreasing along with increasing number of sites in the cluster, which depends on small parameter. The computation accuracy is determined by renormalization precision of the vertex parts of the mass operators of electron-electron and electron-phonon interactions. This accuracy also can be determined by small parameter of cluster expansion for Green’s functions of electrons and phonons. It was found the nature of spin-dependent electron transport in carbon nanotubes with chromium atoms, which are adsorbed on the surface. We show that the phenomenon of spin-dependent electron transport in a carbon nanotube was the result of strong electron correlations, caused by the presence of chromium atoms. The value of the spin polarization of electron transport is determined by the difference of the partial densities of electron states with opposite spin projection at the Fermi level. It is also determined by the difference between the relaxation times arising from different occupation numbers of single-electron states of carbon and chromium atoms. The value of the electric current spin polarization increases along with Cr atoms concentration and magnitude of the external magnetic field increase.


Primitive Cell Mass Operator Localize Magnetic Moment Chromium Atom Vertex Part 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Abrikosov AA, Gorkov LP, Dzyaloshinski IE (1963) Methods of quantum field theory in statistical physics (edited by Silverman RA). Prentice-Hall, Englewood CliffszbMATHGoogle Scholar
  2. 2.
    Blochl PE (1994) Phys Rev B 50:17953ADSCrossRefGoogle Scholar
  3. 3.
    Chepulskii RV, Butler WH (2005) Phys Rev B 72:134205ADSCrossRefGoogle Scholar
  4. 4.
    Ducastelle F (1974) J Phys C 7:1795ADSCrossRefGoogle Scholar
  5. 5.
    Durgun E, Ciraci S (2006) Phys Rev B 74:125404ADSCrossRefGoogle Scholar
  6. 6.
    Elstner M, Porezag D, Jungnickel G, Elsner J, Haugk M, Frauenheim Th, Suhai S, Seifert G (1998) Phys Rev B 58:7260ADSCrossRefGoogle Scholar
  7. 7.
    Enyaschin A, Gemming S, Heine T, Seifert G, Zhechkov L (2006) Phys Chem Chem Phys 8:3320CrossRefGoogle Scholar
  8. 8.
    Harrison WA (1966) Pseudopotentials in the theory of metals. Benjamin, New YorkGoogle Scholar
  9. 9.
    Ivanovskaya VV, Seifert G (2004) Solid State Commun 130:175ADSCrossRefGoogle Scholar
  10. 10.
    Ivanovskaya VV, Heine T, Gemming S, Seifert G (2006) Phys Status Solidi B 243:1757ADSCrossRefGoogle Scholar
  11. 11.
    Ivanovskaya VV, Köhler C, Seifert G (2007) Phys Rev B 75:075410ADSCrossRefGoogle Scholar
  12. 12.
    Johnson DD, Nicholson DM, Pinski FJ, Gyorffy BL, Stocks GM (1990) Phys Rev B 41:9701ADSCrossRefGoogle Scholar
  13. 13.
    Jones RO, Gunnarsson O (1989) Rev Mod Phys 61:689ADSCrossRefGoogle Scholar
  14. 14.
    Köhler C, Seifert G, Gerstmann U, Elstner M, Overhof H, Frauenheim Th (2001) Phys Chem Chem Phys 3:5109CrossRefGoogle Scholar
  15. 15.
    Kohn W, Sham LJ (1965) Phys Rev 140:A1133ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    Kresse G, Joubert D (1999) Phys Rev B 59:1758ADSCrossRefGoogle Scholar
  17. 17.
    Kruchinin SP (1995) Modern Phys Lett B 9:205–215ADSGoogle Scholar
  18. 18.
    Kruchinin SP (2014) Rev Theor Phys 2:124–145Google Scholar
  19. 19.
    Kruchinin S, Nagao H, Aono S ( 2010) Modern aspects of superconductivity: theory of Superconductivity. World Scientific, Singapore, p 220CrossRefGoogle Scholar
  20. 20.
    Kubo R (1957) J Phys Soc Jpn 12:570ADSCrossRefGoogle Scholar
  21. 21.
    Laasonen K, Car R, Lee C, Vanderbilt D (1991) Phys Rev B 43:6796ADSCrossRefGoogle Scholar
  22. 22.
    Los’ VF, Repetsky SP (1994) J Phys Condens Matter 6:1707Google Scholar
  23. 23.
    Perdew JP, Burke K, Ernzerhof M (1996) Phys Rev Lett 77:3865ADSCrossRefGoogle Scholar
  24. 24.
    Perdew JP, Kurth S, Zupan A, Blaha P (1999) Phys Rev Lett 82:2544ADSCrossRefGoogle Scholar
  25. 25.
    Perdew JP, Ruzsinszky A, Csonka GI, Constantin LA, Sun J (2009) Phys Rev Lett 103:026403ADSCrossRefGoogle Scholar
  26. 26.
    Porezag D, Frauenheim T, Köhler T, Seifert G, Kascher R (1995) Phys Rev B 51:2947CrossRefGoogle Scholar
  27. 27.
    Razee SSA, Staunton JB, Ginatempo B, Bruno E, Pinski FJ (2001) J Phys: Condens Matter 13:8565ADSGoogle Scholar
  28. 28.
    Repetsky SP, Shatnii TD (2002) Theor Math Phys 131:456CrossRefGoogle Scholar
  29. 29.
    Sharma RR (1979) Phys Rev B 19:2813ADSCrossRefGoogle Scholar
  30. 30.
    Slater JC (1963) Quantum theory of molecules and solids: electronic structure of molecules, vol 1. McGraw-Hill, New YorkzbMATHGoogle Scholar
  31. 31.
    Slater JC, Koster GF (1954) Phys Rev 94:1498ADSCrossRefGoogle Scholar
  32. 32.
    Staunton JB, Razee SSA, Ling MF, Johnson DD, Pinski FJ (1998) J Phys D: Appl Phys 31:2355ADSCrossRefGoogle Scholar
  33. 33.
    Stocks GM, Winter H (1982) Z Phys B 46:95ADSCrossRefGoogle Scholar
  34. 34.
    Stocks GM, Temmerman WM, Gyorffy BL (1978) Phys Rev Lett 41:339ADSCrossRefGoogle Scholar
  35. 35.
    Sun J, Marsman M, Csonka GI, Ruzsinszky A, Hao P, Kim Y-S, Kresse G, Perdew JP (2011) Phys Rev B 84:035117ADSCrossRefGoogle Scholar
  36. 36.
    Tao J, Perdew JP, Staroverov VN, Scuseria GE (2003) Phys Rev Lett 91:146401ADSCrossRefGoogle Scholar
  37. 37.
    Vanderbilt D (1985) Phys Rev B 41:7892ADSCrossRefGoogle Scholar
  38. 38.
    Wigner EP (1959) Group theory. Academic Press, New York/LondonzbMATHGoogle Scholar
  39. 39.
    Yang C, Zhao J, Lu JP (2003) Phys Rev Lett 90:57203–1Google Scholar
  40. 40.
    Yang C, Zhao J, Lu JP (2004) Nano Lett 4:561ADSCrossRefGoogle Scholar
  41. 41.
    Zubarev DN (1974) Nonequilibrium statistical thermodynamics (edited by Gray P, Shepherd PJ). Consultants Bureau, New YorkGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • S. P. Kruchinin
    • 1
  • S. P. Repetsky
    • 2
    Email author
  • I. G. Vyshyvana
    • 3
  1. 1.Bogolyubov Institute for Theoretical PhysicsKievUkraine
  2. 2.Taras Shevchenko Kiev National UniversityKievUkraine
  3. 3.Institute of High TechnologiesTaras Shevchenko Kiev National UniversityKievUkraine

Personalised recommendations