Skip to main content
Log in

Goos-Hänchen-like shifts for Dirac fermions in monolayer graphene barrier

The European Physical Journal B Aims and scope Submit manuscript

Abstract.

The quantum Goos-Hänchen effect in graphene is found to be the lateral shift of Dirac fermions on the total reflection at a single p-n interface. In this paper, we investigate the lateral shifts of Dirac fermions in transmission through a monolayer graphene barrier. Compared to the smallness of the lateral shifts in total reflection, the lateral shifts can be enhanced by the transmission resonances when the incidence angle is less than the critical angle for total reflection. It is also found that the lateral shifts, as the function of the barrier’s width and incidence angle, can be negative and positive in the cases of Klein tunneling and classical motion. The modulation of the lateral shifts can be realized by changing the electrostatic potential and induced gap, which gives rise to some applications in graphene-based devices.

This is a preview of subscription content, log in via an institution to check access.

Access this article

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Quantum-Classical Anologies, edited by D. Dragoman, M. Dragoman (Springer, Berlin, 2004)

  2. S. Datta, Electronic Transport in Mesoscopic Systems (Cambridge University Press, New York, 1996), p. 276

  3. T.K. Gaylord, E.N. Glytsis, G.N. Henderson, K.P. Martin, D.B. Walker, D.W. Wilson, K.F. Brennan, Proc. IEEE 79, 1159 (1991)

    Article  Google Scholar 

  4. H. van Houten, B.J. van Wees, J.E. Mooij, C.W.J. Beenakker, J.G. Williamson, C.T. Foxon, Europhys. Lett. 5, 721 (1988)

    Article  ADS  Google Scholar 

  5. J. Spector, H.L. Stormer, K.W. Baldwin, L.N. Pfeiffer, K.W. West, Appl. Phys. Lett. 56, 1290 (1990)

    Article  ADS  Google Scholar 

  6. J. Spector, H.L. Stormer, K.W. Baldwin, L.N. Pfeiffer, K.W. West, Appl. Phys. Lett. 58, 263 (1991)

    Article  ADS  Google Scholar 

  7. U. Sivan, M. Heiblum, C.P. Umbach, H. Shtrikman, Phys. Rev. B 41, R7937 (1990)

    Article  ADS  Google Scholar 

  8. L.W. Molenkamp, A.A.M. Staring, C.W.J. Beenakker, R. Eppenga, C.E. Timmering, J.G. Williamson, C.J.P.M. Harmans, C.T. Foxon, Phys. Rev. B 41, R1274 (1990)

    Article  ADS  Google Scholar 

  9. A. Yacoby, M. Heiblum, V. Umansky, H. Shtrikman, D. Mahalu, Phys. Rev. Lett. 73, 3149 (1994)

    Article  ADS  Google Scholar 

  10. Y. Ji, Y. Chung, D. Sprinzak, M. Heiblum, D. Mahalu, H. Shtrikman, Nature 422, 415 (2003)

    Article  ADS  Google Scholar 

  11. A.H. Castro Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, A.K. Geim, Rev. Mod. Phys. 81, 109 (2009)

    Article  ADS  Google Scholar 

  12. C.W. Beenakker, Rev. Mod. Phys. 80, 1337 (2008)

    Article  ADS  Google Scholar 

  13. 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)

    Article  ADS  Google Scholar 

  14. K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, M.I. Katsnelson, I.V. Grigorieva, S.V. Dubonons, A.A. Firsov, Nature (London) 438, 197 (2005)

    Article  ADS  Google Scholar 

  15. Y. Zhang, Y.W. Tan, H.L. Stormer, P. Kim, Nature (London) 438, 201 (2005)

    Article  ADS  Google Scholar 

  16. M.I. Katsnelson, K.S. Novoselov, A.K. Geim, Nat. Phys. 2, 620 (2006)

    Article  Google Scholar 

  17. D.Ö. Güney, D.A. Meyer, Phys. Rev. A 79, 063834 (2009)

    Article  ADS  Google Scholar 

  18. V.V. Cheianov, V. Fal’ko, B.L. Altshuler, Science 315, 1252 (2007)

    Article  ADS  Google Scholar 

  19. C.H. Park, Y.W. Son, L. Yang, M.L. Cohen, S.G. Louie, Nano Lett. 8, 2920 (2008)

    Article  ADS  Google Scholar 

  20. A.V. Shytov, M.S. Rudner, L.S. Levitov, Phys. Rev. Lett. 101, 156804 (2008)

    Article  ADS  Google Scholar 

  21. P. Darancet, V. Olevano, D. Mayou, Phys. Rev. Lett. 102, 136803 (2009)

    Article  ADS  Google Scholar 

  22. S. Ghosh, M. Sharma, J. Phys.: Condens. Matter 21, 292204 (2009)

    Article  Google Scholar 

  23. F.M. Zhang, Y. He, X. Chen, Appl. Phys. Lett. 94, 212105 (2009)

    Article  ADS  Google Scholar 

  24. L. Zhao, S.F. Yelin, Phys. Rev. B 81, 115441 (2010), arXiv:0804.2225v2

    Article  ADS  Google Scholar 

  25. C.W.J. Beenakker, R.A. Sepkhanov, A.R. Akhmerov, J. Tworzydło, Phys. Rev. Lett. 102, 146804 (2009)

    Article  ADS  Google Scholar 

  26. M. Sharma, S. Ghosh, arXiv: 0907.1631v2

  27. F. Goos, H. Hänchen, Ann. Phys. (Leipzig) 436, 333 (1947)

    Article  ADS  Google Scholar 

  28. X. Chen, C.-F. Li, Y. Ban, Phys. Lett. A 354, 161 (2006)

    Article  ADS  Google Scholar 

  29. X. Chen, Y. Ban, C.-F. Li, J. Appl. Phys. 105, 093710 (2009)

    Article  ADS  Google Scholar 

  30. X. Chen, C.-F. Li, Y. Ban, Phys. Rev. B 77, 073307 (2008)

    Article  ADS  Google Scholar 

  31. X. Chen, L.-G. Wang, C.-F. Li, Phys. Rev. A 80, 043839 (2009)

    Article  ADS  Google Scholar 

  32. X. Chen, J.-W. Tao, Appl. Phys. Lett. 94, 262102 (2009)

    Article  ADS  Google Scholar 

  33. S.Y. Zhou, G.H. Gweon, A.V. Federov, P.N. First, W.A. de Heer, D.H. Lee, F. Guinea, A.H. Castro Neto, A. Lanzara, Nat. Mater. 6, 770 (2007)

    Article  ADS  Google Scholar 

  34. M.R. Setare, D. Jahani, J. Phys.: Condens. Matter 22, 245503 (2010)

    Article  ADS  Google Scholar 

  35. M. Esmailpour, A. Esmailpour, R. Asgari, M. Elahi, M.R.R. Tabar, Solid State Commun. 150, 655 (2010)

    Article  ADS  Google Scholar 

  36. C.L. Kane, E.J. Mele, Phys. Rev. Lett. 95, 226801 (2005)

    Article  ADS  Google Scholar 

  37. D. Bohm, Quantum Theory, Prentice-Hall (New York, 1951), pp. 257-261

  38. B. Huard, J.A. Sulpizio, N. Stander, K. Todd, B. Yang, D. Goldhaber-Gordon, Phys. Rev. Lett. 98, 236803 (2007)

    Article  ADS  Google Scholar 

  39. L.-G. Wang, S.-Y. Zhu, Phys. Rev. B 81, 205444 (2010)

    Article  ADS  Google Scholar 

  40. Z.-F. Wang, F. Liu, ACS Nano 4, 2459 (2010)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to X. Chen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, X., Tao, JW. & Ban, Y. Goos-Hänchen-like shifts for Dirac fermions in monolayer graphene barrier. Eur. Phys. J. B 79, 203–208 (2011). https://doi.org/10.1140/epjb/e2010-10553-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjb/e2010-10553-6

Keywords

Navigation