Advertisement

Persistent current of relativistic electrons on a Dirac ring in presence of impurities

  • Sumit Ghosh
  • Arijit SahaEmail author
Regular Article

Abstract

We study the behaviour of persistent current of relativistic electrons on a one dimensional ring in presence of attractive/repulsive scattering potentials. In particular, we investigate the persistent current in accordance with the strength as well as the number of the scattering potential. We find that in presence of single scatterer the persistent current becomes smaller in magnitude than the scattering free scenario. This behaviour is similar to the non-relativistic case. Even for a very strong scattering potential, finite amount of persistent current remains for a relativistic ring. In presence of multiple scatterer we observe that the persistent current is maximum when the scatterers are placed uniformly compared to the current averaged over random configurations. However if we increase the number of scatterers, we find that the random averaged current increases with the number of scatterers. The latter behaviour is in contrast to the non-relativistic case.

Keywords

Mesoscopic and Nanoscale Systems 

References

  1. 1.
    M. Büttiker, Y. Imry, R. Landauer, Phys. Lett. A 96, 365 (1983)ADSCrossRefGoogle Scholar
  2. 2.
    R. Landauer, M. Büttiker, Phys. Rev. Lett. 54, 2049 (1985)ADSCrossRefGoogle Scholar
  3. 3.
    H.F. Cheung, Y. Gefen, E.K. Riedel, W.H. Shih, Phys. Rev. B 37, 6050 (1988)ADSCrossRefGoogle Scholar
  4. 4.
    H.F. Cheung, E.K. Riedel, Y. Gefen, Phys. Rev. Lett. 62, 587 (1989)ADSCrossRefGoogle Scholar
  5. 5.
    A. Altland, S. Iida, A. Müeller-Groeling, H.A. Weidenmüller, Ann. Phys. 219, 148 (1992)ADSCrossRefGoogle Scholar
  6. 6.
    A. Altland, S. Iida, A. Müeller-Groeling, H.A. Weidenmüller, Europhys. Lett. 20, 155 (1992)ADSCrossRefGoogle Scholar
  7. 7.
    J.F. Weisz, R. Kishore, F.V. Kusmartsev, Phys. Rev. B 49, 8126 (1994)ADSCrossRefGoogle Scholar
  8. 8.
    W. Rabaud, L. Saminadayar, D. Mailly, K. Hasselbach, A. Benoit, B. Etienne, Phys. Rev. Lett. 86, 3124 (2001)ADSCrossRefGoogle Scholar
  9. 9.
    M. Moskalets, M. Büttiker, Phys. Rev. B 66, 245321 (2002)ADSCrossRefGoogle Scholar
  10. 10.
    J. Splettstoesser, M. Governale, U. Zülicke, Phys. Rev. B 68, 165341 (2003)ADSCrossRefGoogle Scholar
  11. 11.
    I.O. Kulik, Low Temp. Phys. 36, 841 (2010)ADSCrossRefGoogle Scholar
  12. 12.
    L.P. Levy, G. Dolan, J. Dunsmuir, H. Bouchiat, Phys. Rev. Lett. 64, 2074 (1990)ADSCrossRefGoogle Scholar
  13. 13.
    D. Mailly, C. Chapelier, A. Benoit, Phys. Rev. Lett. 70, 2020 (1993)ADSCrossRefGoogle Scholar
  14. 14.
    N.A.J.M. Kleemans et al., Phys. Rev. Lett. 99, 146808 (2007)ADSCrossRefGoogle Scholar
  15. 15.
    A.C. Bleszynski-Jayich et al., Science 326, 272 (2009)ADSCrossRefGoogle Scholar
  16. 16.
    M. Szopa, M. Margańska, E. Zipper, Phys. Lett. A 299, 593 (2002)ADSCrossRefGoogle Scholar
  17. 17.
    S. Latil, S. Roche, A. Rubio, Phys. Rev. B 67, 165420 (2003)ADSCrossRefGoogle Scholar
  18. 18.
    R.B. Chena, B.J. Lub, C.C. Tsaib, C.P. Changc, F.L. Shyud, M.F. Lin, Carbon 42, 2873 (2004)CrossRefGoogle Scholar
  19. 19.
    I.I. Cotaescu, E. Papp, J. Phys.: Condens. Matter 19, 242206 (2007)ADSGoogle Scholar
  20. 20.
    S. Ghosh, Adv. Condens. Mater. Phys. 2013, 592402 (2013)Google Scholar
  21. 21.
    D. Sticlet, B. Dora, J. Cayssol, Phys. Rev. B 88, 205401 (2013)ADSCrossRefGoogle Scholar
  22. 22.
    K. Ino, Phys. Rev. Lett. 81, 1078 (1998)ADSCrossRefGoogle Scholar
  23. 23.
    K. Ino, Phys. Rev. Lett. 81, 5908 (1998)ADSCrossRefGoogle Scholar
  24. 24.
    K. Ino, Phys. Rev. B 62, 6936 (2000)ADSCrossRefGoogle Scholar
  25. 25.
    A.H. Castro Neto, F. Guinea, N.M.R. Peres, Phys. Rev. B 73, 205408 (2006)ADSCrossRefGoogle Scholar
  26. 26.
    P. Recher, B. Trauzettel, A. Rycerz, Ya.M. Blanter, C.W.J. Beenakker, A.F. Morpurgo, Phys. Rev. B 76, 235404 (2007)ADSCrossRefGoogle Scholar
  27. 27.
    M. Zarenia, J.M. Pereira Jr., F.M. Peeters, G.A. Farias, Nano Lett. 9, 4088 (2009)ADSCrossRefGoogle Scholar
  28. 28.
    M. Zarenia, J.M. Pereira, A. Chaves, F.M. Peeters, G.A. Farias, Phys. Rev. B 81, 045431 (2010)ADSCrossRefGoogle Scholar
  29. 29.
    B.-L. Huang, M.-C. Chang, C.-Y. Mou, J. Phys.: Condens. Matter 24, 245304 (2012)ADSGoogle Scholar
  30. 30.
    P. Michetti, P. Recher, Phys. Rev. B 83, 125420 (2011)ADSCrossRefGoogle Scholar
  31. 31.
    B.H.J. McKellar, G.J. Stephenson Jr., Phys. Rev. C 35, 2262 (1987)ADSCrossRefMathSciNetGoogle Scholar
  32. 32.
    M. Barbier, F.M. Peeters, P. Vasilopoulos, J. Milton Pereira Jr., Phys. Rev. B 77, 115446 (2008)ADSCrossRefGoogle Scholar
  33. 33.
    M. Barbier, P. Vasilopoulos, F.M. Peeters, Phys. Rev. B 80, 205415 (2009)ADSCrossRefGoogle Scholar
  34. 34.
    M. Barbier, P. Vasilopoulos, F.M. Peeters, Phys. Rev. B 82, 235408 (2010)ADSCrossRefGoogle Scholar
  35. 35.
    M.R. Masir, P. Vasilopoulos, F.M. Peeters, J. Phys.: Condens. Matter 22, 465302 (2010)Google Scholar
  36. 36.
    S. Gattenlöhner, W. Belzig, M. Titov, Phys. Rev. B 82, 155417 (2010)ADSCrossRefGoogle Scholar
  37. 37.
    A. Matulis, M.R. Masir, F.M. Peeters, Phys. Rev. A 86, 022101 (2012)ADSCrossRefGoogle Scholar
  38. 38.
    C. Kittel, Introduction to Solid State Physics (John Wiley & Sons, 2004)Google Scholar
  39. 39.
    M.R. Setare, D. Jahani, Physica B 405, 1433 (2010)ADSCrossRefGoogle Scholar
  40. 40.
    J.M. Pereira Jr., P. Vasilopoulos, F.M. Peeters, Appl. Phys. Lett. 90, 132122 (2007)ADSCrossRefGoogle Scholar
  41. 41.
    Lijie Ci et al., Nat. Mater. 9, 430 (2010)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.S.N. Bose National Centre for Basic SciencesSalt LakeIndia
  2. 2.Department of PhysicsUniversity of BaselBaselSwitzerland

Personalised recommendations