Skip to main content

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

The European Physical Journal B volume 87, Article number: 167 (2014) Cite this 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.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

References

  1. M. Büttiker, Y. Imry, R. Landauer, Phys. Lett. A 96, 365 (1983)

    Article  ADS  Google Scholar 

  2. R. Landauer, M. Büttiker, Phys. Rev. Lett. 54, 2049 (1985)

    Article  ADS  Google Scholar 

  3. H.F. Cheung, Y. Gefen, E.K. Riedel, W.H. Shih, Phys. Rev. B 37, 6050 (1988)

    Article  ADS  Google Scholar 

  4. H.F. Cheung, E.K. Riedel, Y. Gefen, Phys. Rev. Lett. 62, 587 (1989)

    Article  ADS  Google Scholar 

  5. A. Altland, S. Iida, A. Müeller-Groeling, H.A. Weidenmüller, Ann. Phys. 219, 148 (1992)

    Article  ADS  Google Scholar 

  6. A. Altland, S. Iida, A. Müeller-Groeling, H.A. Weidenmüller, Europhys. Lett. 20, 155 (1992)

    Article  ADS  Google Scholar 

  7. J.F. Weisz, R. Kishore, F.V. Kusmartsev, Phys. Rev. B 49, 8126 (1994)

    Article  ADS  Google Scholar 

  8. W. Rabaud, L. Saminadayar, D. Mailly, K. Hasselbach, A. Benoit, B. Etienne, Phys. Rev. Lett. 86, 3124 (2001)

    Article  ADS  Google Scholar 

  9. M. Moskalets, M. Büttiker, Phys. Rev. B 66, 245321 (2002)

    Article  ADS  Google Scholar 

  10. J. Splettstoesser, M. Governale, U. Zülicke, Phys. Rev. B 68, 165341 (2003)

    Article  ADS  Google Scholar 

  11. I.O. Kulik, Low Temp. Phys. 36, 841 (2010)

    Article  ADS  Google Scholar 

  12. L.P. Levy, G. Dolan, J. Dunsmuir, H. Bouchiat, Phys. Rev. Lett. 64, 2074 (1990)

    Article  ADS  Google Scholar 

  13. D. Mailly, C. Chapelier, A. Benoit, Phys. Rev. Lett. 70, 2020 (1993)

    Article  ADS  Google Scholar 

  14. N.A.J.M. Kleemans et al., Phys. Rev. Lett. 99, 146808 (2007)

    Article  ADS  Google Scholar 

  15. A.C. Bleszynski-Jayich et al., Science 326, 272 (2009)

    Article  ADS  Google Scholar 

  16. M. Szopa, M. Margańska, E. Zipper, Phys. Lett. A 299, 593 (2002)

    Article  ADS  Google Scholar 

  17. S. Latil, S. Roche, A. Rubio, Phys. Rev. B 67, 165420 (2003)

    Article  ADS  Google Scholar 

  18. R.B. Chena, B.J. Lub, C.C. Tsaib, C.P. Changc, F.L. Shyud, M.F. Lin, Carbon 42, 2873 (2004)

    Article  Google Scholar 

  19. I.I. Cotaescu, E. Papp, J. Phys.: Condens. Matter 19, 242206 (2007)

    ADS  Google Scholar 

  20. S. Ghosh, Adv. Condens. Mater. Phys. 2013, 592402 (2013)

    Google Scholar 

  21. D. Sticlet, B. Dora, J. Cayssol, Phys. Rev. B 88, 205401 (2013)

    Article  ADS  Google Scholar 

  22. K. Ino, Phys. Rev. Lett. 81, 1078 (1998)

    Article  ADS  Google Scholar 

  23. K. Ino, Phys. Rev. Lett. 81, 5908 (1998)

    Article  ADS  Google Scholar 

  24. K. Ino, Phys. Rev. B 62, 6936 (2000)

    Article  ADS  Google Scholar 

  25. A.H. Castro Neto, F. Guinea, N.M.R. Peres, Phys. Rev. B 73, 205408 (2006)

    Article  ADS  Google Scholar 

  26. P. Recher, B. Trauzettel, A. Rycerz, Ya.M. Blanter, C.W.J. Beenakker, A.F. Morpurgo, Phys. Rev. B 76, 235404 (2007)

    Article  ADS  Google Scholar 

  27. M. Zarenia, J.M. Pereira Jr., F.M. Peeters, G.A. Farias, Nano Lett. 9, 4088 (2009)

    Article  ADS  Google Scholar 

  28. M. Zarenia, J.M. Pereira, A. Chaves, F.M. Peeters, G.A. Farias, Phys. Rev. B 81, 045431 (2010)

    Article  ADS  Google Scholar 

  29. B.-L. Huang, M.-C. Chang, C.-Y. Mou, J. Phys.: Condens. Matter 24, 245304 (2012)

    ADS  Google Scholar 

  30. P. Michetti, P. Recher, Phys. Rev. B 83, 125420 (2011)

    Article  ADS  Google Scholar 

  31. B.H.J. McKellar, G.J. Stephenson Jr., Phys. Rev. C 35, 2262 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  32. M. Barbier, F.M. Peeters, P. Vasilopoulos, J. Milton Pereira Jr., Phys. Rev. B 77, 115446 (2008)

    Article  ADS  Google Scholar 

  33. M. Barbier, P. Vasilopoulos, F.M. Peeters, Phys. Rev. B 80, 205415 (2009)

    Article  ADS  Google Scholar 

  34. M. Barbier, P. Vasilopoulos, F.M. Peeters, Phys. Rev. B 82, 235408 (2010)

    Article  ADS  Google Scholar 

  35. M.R. Masir, P. Vasilopoulos, F.M. Peeters, J. Phys.: Condens. Matter 22, 465302 (2010)

    Google Scholar 

  36. S. Gattenlöhner, W. Belzig, M. Titov, Phys. Rev. B 82, 155417 (2010)

    Article  ADS  Google Scholar 

  37. A. Matulis, M.R. Masir, F.M. Peeters, Phys. Rev. A 86, 022101 (2012)

    Article  ADS  Google Scholar 

  38. C. Kittel, Introduction to Solid State Physics (John Wiley & Sons, 2004)

  39. M.R. Setare, D. Jahani, Physica B 405, 1433 (2010)

    Article  ADS  Google Scholar 

  40. J.M. Pereira Jr., P. Vasilopoulos, F.M. Peeters, Appl. Phys. Lett. 90, 132122 (2007)

    Article  ADS  Google Scholar 

  41. Lijie Ci et al., Nat. Mater. 9, 430 (2010)

    Article  ADS  Google Scholar 

Download references

Author information

Author notes

  1. Sumit Ghosh

    Present address: PSE Division, King Abdullah University of Science and Technology, Thuwal, 23955-6900, Saudi Arabia

Authors and Affiliations

  1. S.N. Bose National Centre for Basic Sciences, Salt Lake, 700098, Kolkata, India

    Sumit Ghosh

  2. Department of Physics, University of Basel, Klingelbergstrasse 82, 4056, Basel, Switzerland

    Arijit Saha

Authors
  1. Sumit Ghosh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Arijit Saha
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Arijit Saha.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Ghosh, S., Saha, A. Persistent current of relativistic electrons on a Dirac ring in presence of impurities. Eur. Phys. J. B 87, 167 (2014). https://doi.org/10.1140/epjb/e2014-50223-1

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2014-50223-1

Keywords

  • Mesoscopic and Nanoscale Systems