Electronic transport in graphene nanoribbons with disorder look at the pseudo-spin polarization: Dirac versus tight-binding model

  • Luis I. A. López
  • Michel Mendoza
Regular Article


We have compared results of electronic transport using two different approaches: Dirac vs tight-binding (TB) Hamiltonians to assesses disorder-induced effects in graphene nanoribbons. We apply the proposed Hamiltonians to calculate the density of states, the transmission along the ribbon, and the pseudo-spin polarization (P(E)) in metallic armchair graphene nanoribbons. We clearly show differences between these two approaches in the interference processes, especially in the low-lying energy limit, when the systems are found in the presence of random impurities (disorder). This allows us to find fingerprints associated with each model used. As the disorder increases, more robust electronic transmission (through polarized states in a given sublattice) arises when one is dealing with the Dirac model only. We also find with this model unexpected peaks in the P(E) far from the Dirac point for wider nanoribbons. In the other hand, the model TB show the Dirac limit with disturbances of the hyperboloid subbands for certain potentials of the impurities. In general, our study is indicating that a P(E) spectroscopy (analyzing the line width and intensity) can be used to detect fingerprints of the increase of asymmetry in the scattering processes and the transport limits where hyperboloid subbands are important.


Mesoscopic and Nanoscale Systems 


  1. 1.
    A.H. Castro Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, A.K. Geim, Rev. Mod. Phys. 81, 109 (2009) ADSCrossRefGoogle Scholar
  2. 2.
    M.Z. Hasan, C.L. Kane, Rev. Mod. Phys. 82, 3045 (2010) ADSCrossRefGoogle Scholar
  3. 3.
    A. Kara, H. Enriquez, A.P. Seitsonen, L.C.L.Y. Voon, S. Vizzini, B. Aufray, H. Oughaddou, Surf. Sci. Rep. 67, 141 (2012) ADSCrossRefGoogle Scholar
  4. 4.
    Y. Xu, J. Dai, X.C. Zeng J. Phys. Chem. Lett 6, 1996 (2015) CrossRefGoogle Scholar
  5. 5.
    L. Brey, H.A. Fertig, Phys. Rev. B 73, 235411 (2006) ADSCrossRefGoogle Scholar
  6. 6.
    M. Ezawa, N. Nagaosa, arXiv:1301.6337 (2013)
  7. 7.
    A.K. Geim, A.H. MacDonald, Phys. Today 60, 35 (2007) Google Scholar
  8. 8.
    S. Reich, J. Maultzsch, C. Thomsen, P. Ordejn, Phys. Rev. B 66, 035412 (2002) ADSCrossRefGoogle Scholar
  9. 9.
    Y. Hancock, A. Uppstu, K. Saloriutta, A. Harju, M.J. Puska, Phys. Rev. B 81, 245402 (2010) ADSCrossRefGoogle Scholar
  10. 10.
    L.I.A. López, A. Champi, S. Ujevic, M. Mendoza, Eur. Phys. J. B 88, 298 (2015) ADSCrossRefGoogle Scholar
  11. 11.
    L. Majidi, M. Zareyan, Phys. Rev. B 83, 115422 (2011) ADSCrossRefGoogle Scholar
  12. 12.
    H. Min, G. Borghi, M. Polini, A.H. MacDonald, Phys. Rev. B 77, 041407(R) (2008) ADSCrossRefGoogle Scholar
  13. 13.
    S.H. Abedinpour, M. Polini, A.H. MacDonald, B. Tanatar, M.P. Tosi, G. Vignale, Phys. Rev. Lett. 99, 206802 (2007) ADSCrossRefGoogle Scholar
  14. 14.
    E.R. Mucciolo, A.H. Castro Neto, C.H. Lewenkopf, Phys. Rev. B 79, 075407 (2009) ADSCrossRefGoogle Scholar
  15. 15.
    D. Pesin, A.H. MacDonald, Nat. Mater. 11, 409 (2012) ADSCrossRefGoogle Scholar
  16. 16.
    L.I.A. López, S.M. Yaro, A. Champi, S. Ujevic, M. Mendoza, J. Phys.: Condens. Matter 26, 065301 (2014) Google Scholar
  17. 17.
    C. Lin, Y. Feng, Y. Xiao, M. Drr, X. Huang, X. Xu, R. Zhao, E. Wang, X.-Z. Li, Z. Hu, Nano Lett. 15, 903 (2015) ADSCrossRefGoogle Scholar
  18. 18.
    D.Y. Usachov, A.V. Fedorov, O.Y. Vilkov, A.E. Petukhov, A.G. Rybkin, A. Ernst, M.M. Otrokov, E.V. Chulkov, I.I. Ogorodnikov, M.V. Kuznetsov, L.V. Yashina, E.Yu. Kataev, A.V. Erofeevskaya, V.Y. Voroshnin, V.K. Adamchuk, C. Laubschat, D.V. Vyalikh, Nano Lett. 16, 4535 (2016) ADSCrossRefGoogle Scholar
  19. 19.
    J.A. Lawlor, P.D. Gorman, S.R. Power, C.G. Bezerra, M.S. Ferreira, Carbon 77, 645 (2014) CrossRefGoogle Scholar
  20. 20.
    A. Zabet-Khosousi, L. Zhao, L. Plov, M.S. Hybertsen, D.R. Reichman, A.N. Pasupathy, G.W. Flynn, J. Am. Chem. Soc. 136 1391 (2014) CrossRefGoogle Scholar
  21. 21.
    A. Celis, M.N. Nair, A. Taleb-Ibrahimi, E.H. Conrad, C. Berger, W.A. de Heer, A. Tejeda, J. Phys. D: Appl. Phys. 49, 143001 (2016) ADSCrossRefGoogle Scholar
  22. 22.
    Y.W. Son, M.L. Cohen, S.G. Louie, Phys. Rev. Lett. 97, 216803 (2006) ADSCrossRefGoogle Scholar
  23. 23.
    R. Stacey, Phys. Rev. D 26, 468 (1982) ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    L. Susskind, Phys. Rev. D 16, 3031 (1977) ADSCrossRefGoogle Scholar
  25. 25.
    H. Gausterer, C.B. Lang, Phys. Rev. D 36, 1229 (1987) ADSCrossRefGoogle Scholar
  26. 26.
    J.R. Klauder, S. Lee, Phys. Rev. D 45, 2101 (1992) ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    K. Wakabayashi, M. Fujita, H. Ajiki, M. Sigrist, Phys. Rev. B 59, 8271 (1999) ADSCrossRefGoogle Scholar
  28. 28.
    A.V. Rozhkov, S. Savel’ev, F. Nori, Phys. Rev. B 79, 125420 (2009) ADSCrossRefGoogle Scholar
  29. 29.
    H. Zheng, Z.F. Wang, T. Luo, Q.W. Shi, J. Chen, Phys. Rev. B 75, 165414 (2007) ADSCrossRefGoogle Scholar
  30. 30.
    S. Datta, Quantum transport: atom to transistor (Cambridge University Press, Cambridge, 2005) Google Scholar
  31. 31.
    S. Ujevic, M. Mendoza, Phys. Rev. B 82, 035432 (2010) ADSCrossRefGoogle Scholar
  32. 32.
    C.H. Lewenkopf, E.R. Mucciolo, J. Comput. Electron. 12, 203 (2013) CrossRefGoogle Scholar
  33. 33.
    A.L.C. Pereira, P.A. Schulz, Phys. Rev. B 77, 075416 (2008) ADSCrossRefGoogle Scholar
  34. 34.
    M. Mendoza, P.A. Schulz, Phys. Rev. B 68, 205302 (2003) ADSCrossRefGoogle Scholar
  35. 35.
    M.A. Topinka et al., Science 289, 2323 (2000) ADSCrossRefGoogle Scholar
  36. 36.
    D. Ferry, S.M. Goodnick, Transport in nanostructures (Cambridge University Press, Cambridge, 1997) Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Departamento de Física, Universidade Estadual de Ponta GrossaPonta GrossaBrazil
  2. 2.Centro de Ciências Naturais e Humanas, Universidade Federal do ABCSanto AndréBrazil

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