Magnetic dispersion of Dirac fermions in graphene under inhomogeneous field profiles

  • D. JahaniEmail author
  • F. Shahbazi
  • M. R Setare
Regular Article


We address the exact relations for the energy spectrum of massive Dirac fermions of graphene for a class of position-dependent magnetic field profiles, which could be created under inhomogeneous strain fields, with possibility of inducing a Dirac gap. We then show that in the linear regime our results correspond well to the earlier approaches for the massless case. We also prove that our approach for obtaining the relativistic Landau levels of Dirac fermions created by a constant magnetic field together with a spatially varying normal pseudo-magnetic profile, which varies as \( 1/x^2\) , recovers well the earlier results in this regard. It turns out that, in this case, the associated Landau energy levels are obtained by considering two shape-invariant potentials which belong to the family of isotonic oscillators with a set of equally spaced energy levels.


  1. 1.
    K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, A.A. Firsov, Science 306, 666 (2004)ADSCrossRefGoogle Scholar
  2. 2.
    A.K. Geim, K.S. Novoselov, Nat. Mater. 6, 183 (2007)ADSCrossRefGoogle Scholar
  3. 3.
    K.S. Novoselov, D. Jiang, F. Schedin, T.J. Booth, V.V. Khotkevich, S.M. Morozov, A.K. Geim, Proc. Natl. Acad. Sci. U.S.A. 102, 10451 (2005)ADSCrossRefGoogle Scholar
  4. 4.
    G. Cocco, E. Cadelano, L. Colombo, Phys. Rev. B 81, 241412(R) (2010)ADSCrossRefGoogle Scholar
  5. 5.
    F. Guinea, M.I. Katsnelson, A.K. Geim, Nat. Phys. 6, 30 (2010)CrossRefGoogle Scholar
  6. 6.
    Z. Jiang, Y. Zhang, Y.W. Tan, H.L. Stormer, P. Kim, Solid State Commun. 143, 14 (2007)ADSCrossRefGoogle Scholar
  7. 7.
    K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, M.I. Katsnelson, I.V. Grigorieva, S.V. Dubonos, A.A. Firsov, Nature 438, 197 (2005)ADSCrossRefGoogle Scholar
  8. 8.
    A.D. Martino, L. DellAnna, R. Egger, Phys. Rev. Lett. 98, 066802 (2007)ADSCrossRefGoogle Scholar
  9. 9.
    A.D. Martino, L. DellAnna, R. Egger, Solid State Commun. 144, 547 (2007)ADSCrossRefGoogle Scholar
  10. 10.
    N.M.R. Peres, E.V. Castro, J. Phys.: Condens. Matter 19, 406231 (2007)Google Scholar
  11. 11.
    M.R. Masir, P. Vasilopoulos, A. Matulis, F.M. Peeters, Phys. Rev. B 77, 235443 (2008)ADSCrossRefGoogle Scholar
  12. 12.
    C.G. Beneventano, E.M. Santangelo, J. Phys. A 39, 7457 (2006)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    A.H.C. Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, A.K. Geim, Rev. Mod. Phys. 81, 109 (2009)ADSCrossRefGoogle Scholar
  14. 14.
    Y. Zhang, Y.W. Tan, H.L. Stormer, P. Kim, Nature 438, 201 (2005)ADSCrossRefGoogle Scholar
  15. 15.
    M.O. Goerbig, C. R. Phys. 12, 369 (2011)ADSCrossRefGoogle Scholar
  16. 16.
    K.H. Ding, L.K. Lim, G. Su, Z.Y. Weng, arXiv:1709.09010Google Scholar
  17. 17.
    Y. Barlas, K. Yang, A.H. Macdonald, Nanotechnology 23, 052001 (2012)ADSCrossRefGoogle Scholar
  18. 18.
    V.P. Gusynin, S.G. Sharapov, Phys. Rev. Lett. 95, 146801 (2005)ADSCrossRefGoogle Scholar
  19. 19.
    M. Ezawa, Phys. Lett. A 372, 924 (2008)ADSCrossRefGoogle Scholar
  20. 20.
    B. Midya, D.J. Fernndez, J. Phys. A 47, 285302 (2014)MathSciNetCrossRefGoogle Scholar
  21. 21.
    M.R. Setare, D. Jahani, Int. J. Mod. Phys. B 25, 365 (2011)ADSCrossRefGoogle Scholar
  22. 22.
    M.R. Setare, D. Jahani, Chin. Phys. Lett. 28, 097302 (2011)ADSCrossRefGoogle Scholar
  23. 23.
    N.M.R. Peres, A.H.C. Neto, F. Guinea, Phys. Rev. B 73, 241403 (2006)ADSCrossRefGoogle Scholar
  24. 24.
    M.O. Goerbig, Rev. Mod. Phys. 83, 1193 (2011)ADSCrossRefGoogle Scholar
  25. 25.
    E.B. Choubabi, M.E. Bouziani, A. Jellal, Int. J. Geom. Methods Mod. Phys. 7, 909 (2010)MathSciNetCrossRefGoogle Scholar
  26. 26.
    V.M. Pereira, A.H.C. Neto, Phys. Rev. Lett. 103, 046801 (2009)ADSCrossRefGoogle Scholar
  27. 27.
    S. Kuru, J. Negro, L.M. Nieto, J. Phys.: Condens. Matter 21, 455305 (2009)ADSGoogle Scholar
  28. 28.
    L.G.D.S. Leite, C. Filgueiras, D. Cogollo, E.O. Silva, Phys. Lett. A 379, 907 (2015)CrossRefGoogle Scholar
  29. 29.
    M.R. Setare, O. Hatami, Chin. Phys. Lett. 25, 3848 (2008)ADSCrossRefGoogle Scholar
  30. 30.
    M. Eshghi, H. Mehraban, C. R. Phys. 18, 47 (2017)ADSCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Materials and Evergy Research CenterTehranIran
  2. 2.Campus of BijarUniversity of KurdistanBijarIran

Personalised recommendations