Advertisement

Journal of Computational Electronics

, Volume 12, Issue 2, pp 63–75 | Cite as

Transport through quantum spin Hall insulator/metal junctions in graphene ribbons

  • Elsa Prada
  • Georgo Metalidis
Article

Abstract

Quantum spin Hall insulator/metal interfaces are formed in graphene ribbons with intrinsic spin-orbit coupling by selectively doping two regions creating a potential step. For a clean graphene ribbon, the transmission of the topological edge states through a n-n or p-p junction is perfect irrespective of the ribbon termination, width, and potential step parameters due to the orthogonality of incoming and outgoing edge channels. This is shown numerically for an arbitrary crystallographic orientation of the ribbon and proven analytically for zigzag and metallic armchair boundary conditions. In disordered ribbons, the orthogonality between left- and right-movers is in general destroyed and backscattering sets in. However, transmission approaches one by increasing the ribbon’s width, even in the presence of strong edge roughness.

Keywords

Graphene ribbons Quantum spin Hall effect pn Junctions Quantum transport 

Notes

Acknowledgements

E.P. acknowledges the support of the CSIC JAE-Doc program and the Spanish Ministry of Science and Innovation through Grant No. FIS2009-08744.

References

  1. 1.
    Adroguer, P., Grenier, C., Carpentier, D., Cayssol, J., Degiovanni, P., Orignac, E.: Probing the helical edge states of a topological insulator by cooper-pair injection. Phys. Rev. B 82, 081303 (2010) CrossRefGoogle Scholar
  2. 2.
    Akhmerov, A.R., Bardarson, J.H., Rycerz, A., Beenakker, C.W.J.: Theory of the valley-valve effect in graphene nanoribbons. Phys. Rev. B 77, 205416 (2008) CrossRefGoogle Scholar
  3. 3.
    Akhmerov, A.R., Beenakker, C.W.J.: Detection of valley polarization in graphene by a superconducting contact. Phys. Rev. Lett. 98, 157003 (2007) CrossRefGoogle Scholar
  4. 4.
    Bai, C., Wang, J., Jia, S., Yang, Y.: Spin-orbit interaction effects on magnetoresistance in graphene-based ferromagnetic double junctions. Appl. Phys. Lett. 96(22), 223102 (2010) CrossRefGoogle Scholar
  5. 5.
    Beenakker, C.W.J.: Specular Andreev reflection in graphene. Phys. Rev. Lett. 97, 067007 (2006) CrossRefGoogle Scholar
  6. 6.
    Bercioux, D., De Martino, A.: Spin-resolved scattering through spin-orbit nanostructures in graphene. Phys. Rev. B 81, 165410 (2010) CrossRefGoogle Scholar
  7. 7.
    Bernevig, B.A., Zhang, S.C.: Quantum spin Hall effect. Phys. Rev. Lett. 96, 106802 (2006) CrossRefGoogle Scholar
  8. 8.
    Bernevig, B.A., Hughes, T.L., Zhang, S.C.: Quantum spin Hall effect and topological phase transition in hgte quantum wells. Science 314(5806), 1757–1761 (2006) CrossRefGoogle Scholar
  9. 9.
    Boettger, J.C., Trickey, S.B.: First-principles calculation of the spin-orbit splitting in graphene. Phys. Rev. B 75, 121402 (2007) CrossRefGoogle Scholar
  10. 10.
    Brey, L., Fertig, H.A.: Electronic states of graphene nanoribbons studied with the Dirac equation. Phys. Rev. B 73, 235411 (2006) CrossRefGoogle Scholar
  11. 11.
    Castro Neto, A.H., Guinea, F.: Impurity-induced spin-orbit coupling in graphene. Phys. Rev. Lett. 103, 026804 (2009) CrossRefGoogle Scholar
  12. 12.
    Castro Neto, A.H., Guinea, F., Peres, N.M.R., Novoselov, K.S., Geim, A.K.: The electronic properties of graphene. Rev. Mod. Phys. 81, 109–162 (2009) CrossRefGoogle Scholar
  13. 13.
    Cheianov, V., Fal’ko, V., Altshuler, B.: The focusing of electron flow and a Veselago lens in graphene pn junctions. Science 315(5816), 1252 (2007) CrossRefGoogle Scholar
  14. 14.
    Cho, S., Chen, Y., Fuhrer, M.: Gate-tunable graphene spin valve. Appl. Phys. Lett. 91(12), 123105 (2007) CrossRefGoogle Scholar
  15. 15.
    Das Sarma, S., Adam, S., Hwang, E.H., Rossi, E.: Electronic transport in two-dimensional graphene. Rev. Mod. Phys. 83, 407–470 (2011) CrossRefGoogle Scholar
  16. 16.
    Datta, S.: Electronic Transport in Mesoscopic Systems. Cambridge Univ. Press, Cambridge (1997) Google Scholar
  17. 17.
    Fu, L., Kane, C.L.: Josephson current and noise at a superconductor/quantum-spin-hall-insulator/superconductor junction. Phys. Rev. B 79(16), 161408 (2009) CrossRefGoogle Scholar
  18. 18.
    Gmitra, M., Konschuh, S., Ertler, C., Ambrosch-Draxl, C., Fabian, J.: Band-structure topologies of graphene: spin-orbit coupling effects from first principles. Phys. Rev. B 80, 235431 (2009) CrossRefGoogle Scholar
  19. 19.
    Gosalbez-Martinez, D., Soriano, D., Palacios, J.J., Fernandez-Rossier, J.: Spin-filtered edge states in graphene. Solid State Commun. 152(15), 1469–1476 (2012) CrossRefGoogle Scholar
  20. 20.
    Hasan, M.Z., Kane, C.L.: Colloquium: topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010) CrossRefGoogle Scholar
  21. 21.
    Heersche, H., Jarillo-Herrero, P., Oostinga, J., Vandersypen, L., Morpurgo, A.: Bipolar supercurrent in graphene. Nature 446(7131), 56–59 (2007) CrossRefGoogle Scholar
  22. 22.
    Hu, J., Alicea, J., Wu, R., Franz, M.: Giant topological insulator gap in graphene with 5d adatoms (2012). arXiv:1206.4320
  23. 23.
    Huertas-Hernando, D., Guinea, F., Brataas, A.: Spin-orbit coupling in curved graphene, fullerenes, nanotubes, and nanotube caps. Phys. Rev. B 74, 155426 (2006) CrossRefGoogle Scholar
  24. 24.
    Kane, C.L., Mele, E.J.: Quantum spin Hall effect in graphene. Phys. Rev. Lett. 95, 226801 (2005) CrossRefGoogle Scholar
  25. 25.
    Katsnelson, M.I., Novoselov, K.S., Geim, A.K.: Chiral tunnelling and the Klein paradox in graphene. Nat. Phys. 2(9), 620–625 (2006) CrossRefGoogle Scholar
  26. 26.
    Klitzing, K.V., Dorda, G., Pepper, M.: New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance. Phys. Rev. Lett. 45, 494–497 (1980) CrossRefGoogle Scholar
  27. 27.
    Knez, I., Du, R.R., Sullivan, G.: Evidence for helical edge modes in inverted InAs/GaSb quantum wells. Phys. Rev. Lett. 107, 136603 (2011) CrossRefGoogle Scholar
  28. 28.
    König, M., Wiedmann, S., Brüne, C., Roth, A., Buhmann, H., Molenkamp, L.W., Qi, X.L., Zhang, S.C.: Quantum spin Hall insulator state in hgte quantum wells. Science 318(5851), 766–770 (2007) CrossRefGoogle Scholar
  29. 29.
    López-Sancho, M.P., Muñoz, M.C.: Intrinsic spin-orbit interactions in flat and curved graphene nanoribbons. Phys. Rev. B 83, 075406 (2011) CrossRefGoogle Scholar
  30. 30.
    Mahfouzi, F., Nikolić, B.K., Chen, S.H., Chang, C.R.: Microwave-driven ferromagnet-topological-insulator heterostructures: the prospect for giant spin battery effect and quantized charge pump devices. Phys. Rev. B 82, 195440 (2010) CrossRefGoogle Scholar
  31. 31.
    Metalidis, G., Bruno, P.: Green’s function technique for studying electron flow in two-dimensional mesoscopic samples. Phys. Rev. B 72, 235304 (2005) CrossRefGoogle Scholar
  32. 32.
    Miao, F., Wijeratne, S., Zhang, Y., Coskun, U., Bao, W., Lau, C.: Phase-coherent transport in graphene quantum billiards. Science 317(5844), 1530–1533 (2007) CrossRefGoogle Scholar
  33. 33.
    Min, H., Hill, J.E., Sinitsyn, N.A., Sahu, B.R., Kleinman, L., MacDonald, A.H.: Intrinsic and Rashba spin-orbit interactions in graphene sheets. Phys. Rev. B 74, 165310 (2006) CrossRefGoogle Scholar
  34. 34.
    Mondal, S., Sen, D., Sengupta, K., Shankar, R.: Tuning the conductance of Dirac fermions on the surface of a topological insulator. Phys. Rev. Lett. 104(4), 46403 (2010) CrossRefGoogle Scholar
  35. 35.
    Mucciolo, E.R., Castro Neto, A.H., Lewenkopf, C.H.: Conductance quantization and transport gaps in disordered graphene nanoribbons. Phys. Rev. B 79, 075407 (2009) CrossRefGoogle Scholar
  36. 36.
    Novik, E.G., Recher, P., Hankiewicz, E.M., Trauzettel, B.: Signatures of topological order in ballistic bulk transport of hgte quantum wells. Phys. Rev. B 81, 241303 (2010) CrossRefGoogle Scholar
  37. 37.
    Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Katsnelson, M.I., Grigorieva, I.V., Dubonos, S.V., Firsov, A.A.: Two-dimensional gas of massless Dirac fermions in graphene. Nature 438(7065), 197–200 (2005) CrossRefGoogle Scholar
  38. 38.
    Pereg-Barnea, T., Refael, G.: Inducing topological order in a honeycomb lattice. Phys. Rev. B 85, 075127 (2012) CrossRefGoogle Scholar
  39. 39.
    Prada, E., San-Jose, P., Brey, L.: Zero Landau level in folded graphene nanoribbons. Phys. Rev. Lett. 105, 106802 (2010) CrossRefGoogle Scholar
  40. 40.
    Prada, E., San-Jose, P., León, G., Fogler, M.M., Guinea, F.: Singular elastic strains and magnetoconductance of suspended graphene. Phys. Rev. B 81, 161402 (2010) CrossRefGoogle Scholar
  41. 41.
    Prada, E., San-Jose, P., Brey, L., Fertig, H.: Band topology and the quantum spin Hall effect in bilayer graphene. Solid State Commun. 151(16), 1075–1083 (2011) CrossRefGoogle Scholar
  42. 42.
    Roth, A., Brüne, C., Buhmann, H., Molenkamp, L.W., Maciejko, J., Qi, X.L., Zhang, S.C.: Nonlocal transport in the quantum spin Hall state. Science 325(5938), 294–297 (2009) CrossRefGoogle Scholar
  43. 43.
    Stanescu, T., Sau, J., Lutchyn, R., Sarma, S.: Proximity effect at the superconductor–topological insulator interface. Phys. Rev. B 81(24), 241310 (2010) CrossRefGoogle Scholar
  44. 44.
    Ström, A., Johannesson, H.: Tunneling between edge states in a quantum spin Hall system. Phys. Rev. Lett. 102, 096806 (2009) CrossRefGoogle Scholar
  45. 45.
    Tombros, N., Jozsa, C., Popinciuc, M., Jonkman, H., Van Wees, B.: Electronic spin transport and spin precession in single graphene layers at room temperature. Nature 448(7153), 571–574 (2007) CrossRefGoogle Scholar
  46. 46.
    Weeks, C., Hu, J., Alicea, J., Franz, M., Wu, R.: Engineering a robust quantum spin Hall state in graphene via adatom deposition. Phys. Rev. X 1, 021001 (2011) CrossRefGoogle Scholar
  47. 47.
    Xia, F., Perebeinos, V., Lin, Y.M., Wu, Y., Avouris, P.: The origins and limits of metal-graphene junction resistance. Nat. Nanotechnol. 6(3), 179–184 (2011) CrossRefGoogle Scholar
  48. 48.
    Yamakage, A., Imura, K., Cayssol, J., Kuramoto, Y.: Spin-orbit effects in a graphene bipolar pn junction. Europhys. Lett. 87(4), 47005 (2009) CrossRefGoogle Scholar
  49. 49.
    Yamakage, A., Imura, K., Cayssol, J., Kuramoto, Y.: Interfacial charge and spin transport in z_{2} topological insulators. Phys. Rev. B 83(12), 125401 (2011) CrossRefGoogle Scholar
  50. 50.
    Yao, Y., Ye, F., Qi, X.L., Zhang, S.C., Fang, Z.: Spin-orbit gap of graphene: first-principles calculations. Phys. Rev. B 75, 041401 (2007) CrossRefGoogle Scholar
  51. 51.
    Yokoyama, T., Tanaka, Y., Nagaosa, N.: Giant spin rotation in the junction between a normal metal and a quantum spin Hall system. Phys. Rev. Lett. 102(16), 166801 (2009) CrossRefGoogle Scholar
  52. 52.
    Young, A.F., Kim, P.: Quantum interference and Klein tunnelling in graphene heterojunctions. Nat. Phys. 5(3), 222–226 (2009) CrossRefGoogle Scholar
  53. 53.
    Zarea, M., Sandler, N.: Quantum spin Hall phase in neutral zigzag graphene ribbons. Physica B 404(18), 2694–2698 (2009) CrossRefGoogle Scholar
  54. 54.
    Zhang, L., Chang, K., Xie, X., Buhmann, H., Molenkamp, L.: Quantum tunneling through planar p–n junctions in hgte quantum wells. New J. Phys. 12(8), 083058 (2010) CrossRefGoogle Scholar
  55. 55.
    Zhang, Y., Tan, Y.W., Stormer, H.L., Kim, P.: Experimental observation of the quantum Hall effect and Berry’s phase in graphene. Nature 438(7065), 201–204 (2005) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Instituto de Ciencia de Materiales de MadridCSICMadridSpain
  2. 2.Institut für Theoretische Festkörperphysik and DFG-Center for Functional NanostructuresKarlsruhe Institute of Technology (KIT)KarlsruheGermany

Personalised recommendations