Abstract.
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
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)
A.K. Geim, K.S. Novoselov, Nat. Mater. 6, 183 (2007)
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)
G. Cocco, E. Cadelano, L. Colombo, Phys. Rev. B 81, 241412(R) (2010)
F. Guinea, M.I. Katsnelson, A.K. Geim, Nat. Phys. 6, 30 (2010)
Z. Jiang, Y. Zhang, Y.W. Tan, H.L. Stormer, P. Kim, Solid State Commun. 143, 14 (2007)
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)
A.D. Martino, L. DellAnna, R. Egger, Phys. Rev. Lett. 98, 066802 (2007)
A.D. Martino, L. DellAnna, R. Egger, Solid State Commun. 144, 547 (2007)
N.M.R. Peres, E.V. Castro, J. Phys.: Condens. Matter 19, 406231 (2007)
M.R. Masir, P. Vasilopoulos, A. Matulis, F.M. Peeters, Phys. Rev. B 77, 235443 (2008)
C.G. Beneventano, E.M. Santangelo, J. Phys. A 39, 7457 (2006)
A.H.C. Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, A.K. Geim, Rev. Mod. Phys. 81, 109 (2009)
Y. Zhang, Y.W. Tan, H.L. Stormer, P. Kim, Nature 438, 201 (2005)
M.O. Goerbig, C. R. Phys. 12, 369 (2011)
K.H. Ding, L.K. Lim, G. Su, Z.Y. Weng, arXiv:1709.09010
Y. Barlas, K. Yang, A.H. Macdonald, Nanotechnology 23, 052001 (2012)
V.P. Gusynin, S.G. Sharapov, Phys. Rev. Lett. 95, 146801 (2005)
M. Ezawa, Phys. Lett. A 372, 924 (2008)
B. Midya, D.J. Fernndez, J. Phys. A 47, 285302 (2014)
M.R. Setare, D. Jahani, Int. J. Mod. Phys. B 25, 365 (2011)
M.R. Setare, D. Jahani, Chin. Phys. Lett. 28, 097302 (2011)
N.M.R. Peres, A.H.C. Neto, F. Guinea, Phys. Rev. B 73, 241403 (2006)
M.O. Goerbig, Rev. Mod. Phys. 83, 1193 (2011)
E.B. Choubabi, M.E. Bouziani, A. Jellal, Int. J. Geom. Methods Mod. Phys. 7, 909 (2010)
V.M. Pereira, A.H.C. Neto, Phys. Rev. Lett. 103, 046801 (2009)
S. Kuru, J. Negro, L.M. Nieto, J. Phys.: Condens. Matter 21, 455305 (2009)
L.G.D.S. Leite, C. Filgueiras, D. Cogollo, E.O. Silva, Phys. Lett. A 379, 907 (2015)
M.R. Setare, O. Hatami, Chin. Phys. Lett. 25, 3848 (2008)
M. Eshghi, H. Mehraban, C. R. Phys. 18, 47 (2017)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Jahani, D., Shahbazi, F. & Setare, M.R. Magnetic dispersion of Dirac fermions in graphene under inhomogeneous field profiles. Eur. Phys. J. Plus 133, 328 (2018). https://doi.org/10.1140/epjp/i2018-12137-4
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/i2018-12137-4