Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Quantized edge modes in atomic-scale point contacts in graphene

Abstract

The zigzag edges of single- or few-layer graphene are perfect one-dimensional conductors owing to a set of gapless states that are topologically protected against backscattering. Direct experimental evidence of these states has been limited so far to their local thermodynamic and magnetic properties, determined by the competing effects of edge topology and electron–electron interaction. However, experimental signatures of edge-bound electrical conduction have remained elusive, primarily due to the lack of graphitic nanostructures with low structural and/or chemical edge disorder. Here, we report the experimental detection of edge-mode electrical transport in suspended atomic-scale constrictions of single and multilayer graphene created during nanomechanical exfoliation of highly oriented pyrolytic graphite. The edge-mode transport leads to the observed quantization of conductance close to multiples of G0 = 2e2/h. At the same time, conductance plateaux at G0/2 and a split zero-bias anomaly in non-equilibrium transport suggest conduction via spin-polarized states in the presence of an electron–electron interaction.

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

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Mechanical exfoliation process and corresponding evolution of electrical conductance.
Figure 2: Non-equilibrium transport and magneto-conductance in nanoconstrictions.
Figure 3: Fractional quantization of the zero-bias conductance.

Similar content being viewed by others

References

  1. Han, M. Y., Özyilmaz, B., Zhang, Y. & Kim, P. Energy band-gap engineering of graphene nanoribbons. Phys. Rev. Lett. 98, 206805 (2007).

    Article  Google Scholar 

  2. Stampfer, C. et al. Energy gaps in etched graphene nanoribbons. Phys. Rev. Lett. 102, 056403 (2009).

    Article  CAS  Google Scholar 

  3. Todd, K., Chou, H.-T., Amasha, S. & Goldhaber-Gordon, D. Quantum dot behavior in graphene nanoconstrictions. Nano Lett. 9, 416–421 (2009).

    Article  CAS  Google Scholar 

  4. Lin, Y.-M., Perebeinos, V., Chen, Z. & Avouris, P. Electrical observation of subband formation in graphene nanoribbons. Phys. Rev. B 78, 161409 (2008).

    Article  Google Scholar 

  5. Tombros, N. et al. Quantized conductance of a suspended graphene nanoconstriction. Nat. Phys. 7, 697–700 (2011).

    Article  CAS  Google Scholar 

  6. Baringhaus, J. et al. Exceptional ballistic transport in epitaxial graphene nanoribbons. Nature 506, 349–354 (2014).

    Article  CAS  Google Scholar 

  7. Jia, X., Campos-Delgado, J., Terrones, M., Meunier, V. & Dresselhaus, M. S. Graphene edges: a review of their fabrication and characterization. Nanoscale 3, 86–95 (2011).

    Article  CAS  Google Scholar 

  8. 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).

    Article  Google Scholar 

  9. Chen, Z., Lin, Y.-M., Rooks, M. J. & Avouris, P. Graphene nano-ribbon electronics. Physica E 40, 228–232 (2007).

    Article  CAS  Google Scholar 

  10. Kosynkin, D. V. et al. Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons. Nature 458, 872–876 (2009).

    Article  CAS  Google Scholar 

  11. Jiao, L., Zhang, L., Wang, X., Diankov, G. & Dai, H. Narrow graphene nanoribbons from carbon nanotubes. Nature 458, 877–880 (2009).

    Article  CAS  Google Scholar 

  12. Schffel, F. et al. Atomic resolution imaging of the edges of catalytically etched suspended few-layer graphene. ACS Nano. 5, 1975–1983 (2011).

    Article  Google Scholar 

  13. Cai, J. et al. Atomically precise bottom-up fabrication of graphene nanoribbons. Nature 466, 470–473 (2010).

    Article  CAS  Google Scholar 

  14. Sprinkle, M. et al. Scalable templated growth of graphene nanoribbons on SiC. Nat. Nanotech. 5, 727–731 (2010).

    Article  CAS  Google Scholar 

  15. Bischoff, D., Libisch, F., Burgdörfer, J., Ihn, T. & Ensslin, K. Characterizing wave functions in graphene nanodevices: electronic transport through ultrashort graphene constrictions on a boron nitride substrate. Phys. Rev. B 90, 115405 (2014).

    Article  Google Scholar 

  16. Kim, K. et al. Atomically perfect torn graphene edges and their reversible reconstruction. Nat. Commun. 4, 2723 (2013).

    Article  Google Scholar 

  17. Kim, K. et al. Ripping graphene: preferred directions. Nano Lett. 12, 293–297 (2012).

    Article  CAS  Google Scholar 

  18. Girit, Ç. Ö. et al. Graphene at the edge: stability and dynamics. Science 323, 1705–1708 (2009).

    Article  CAS  Google Scholar 

  19. Nakada, K., Fujita, M., Dresselhaus, G. & Dresselhaus, M. S. Edge state in graphene ribbons: nanometer size effect and edge shape dependence. Phys. Rev. B 54, 17954 (1996).

    Article  CAS  Google Scholar 

  20. Ihnatsenka, S. & Kirczenow, G. Conductance quantization in strongly disordered graphene ribbons. Phys. Rev. B 80, 201407 (2009).

    Article  Google Scholar 

  21. Li, J., Martin, I., Buttiker, M. & Morpurgo, A. F. Topological origin of subgap conductance in insulating bilayer graphene. Nat. Phys. 7, 38–42 (2011).

    Article  CAS  Google Scholar 

  22. Sen, D., Novoselov, K. S., Reis, P. M. & Buehler, M. J. Tearing graphene sheets from adhesive substrates produces tapered nanoribbons. Small 6, 1108–1116 (2010).

    Article  CAS  Google Scholar 

  23. Jung, J., Zhang, F., Qiao, Z. & MacDonald, A. H. Valley-Hall kink and edge states in multilayer graphene. Phys. Rev. B 84, 075418 (2011).

    Article  Google Scholar 

  24. Wakabayashi, K., Takane, Y. & Sigrist, M. Perfectly conducting channel and universality crossover in disordered graphene nanoribbons. Phys. Rev. Lett. 99, 036601 (2007).

    Article  Google Scholar 

  25. Castro, E. V., Peres, N. M. R., Lopes dos Santos, J. M. B., Neto, A. H. C. & Guinea, F. Localized states at zigzag edges of bilayer graphene. Phys. Rev. Lett. 100, 026802 (2008).

    Article  Google Scholar 

  26. Jiang, D. E., Sumpter, B. G. & Dai, S. Unique chemical reactivity of a graphene nanoribbon's zigzag edge. J Chem. Phys. 126, 134701 (2007).

    Article  Google Scholar 

  27. Koskinen, P., Malola, S. & Häkkinen, H. Self-passivating edge reconstructions of graphene. Phys. Rev. Lett. 101, 115502 (2008).

    Article  Google Scholar 

  28. Kristensen, A. et al. Bias and temperature dependence of the 0.7 conductance anomaly in quantum point contacts. Phys. Rev. B 62, 10950–10957 (2000).

    Article  CAS  Google Scholar 

  29. Fujita, M., Wakabayashi, K., Nakada, K. & Kusakabe, K. Peculiar localized state at zigzag graphite edge. J. Phys. Soc. Jpn 65, 1920–1923 (1996).

    Article  CAS  Google Scholar 

  30. Son, Y.-W., Cohen, M. L. & Louie, S. G. Half-metallic graphene nanoribbons. Nature 444, 347–349 (2006).

    Article  CAS  Google Scholar 

  31. Tao, C. et al. Spatially resolving edge states of chiral graphene nanoribbons. Nat. Phys. 7, 616–620 (2011).

    Article  CAS  Google Scholar 

  32. Magda, G. Z. et al. Room-temperature magnetic order on zigzag edges of narrow graphene nanoribbons. Nature 514, 608–611 (2014).

    Article  CAS  Google Scholar 

  33. Shklovskii, B. Positive magnetoresistance in the variable-range hopping region. Sov. Phys. Semicond. 17, 1311–1316 (1983).

    Google Scholar 

  34. Ghosh, A., Pepper, M., Beere, H. E. & Ritchie, D. A. Dynamic localization of two-dimensional electrons at mesoscopic length scales. Phys. Rev. B 70, 233309 (2004).

    Article  Google Scholar 

  35. Allen, M. T. et al. Spatially resolved edge currents and guided-wave electronic states in graphene. Nat. Phys. 12, 128–133 (2016).

    Article  CAS  Google Scholar 

  36. Shu, C. et al. Fractional conductance quantization in metallic nanoconstrictions under electrochemical potential control. Phys. Rev. Lett. 84, 5196–5199 (2000).

    Article  CAS  Google Scholar 

  37. Krans, J., Van Ruitenbeek, J., Fisun, V., Yanson, I. & De Jongh, L. The signature of conductance quantization in metallic point contacts. Nature 375, 767–769 (1995).

    Article  CAS  Google Scholar 

  38. Frank, S., Poncharal, P., Wang, Z. & de Heer, W. A. Carbon nanotube quantum resistors. Science 280, 1744–1746 (1998).

    Article  CAS  Google Scholar 

  39. Thomas, K. J. et al. Possible spin polarization in a one-dimensional electron gas. Phys. Rev. Lett. 77, 135–138 (1996).

    Article  CAS  Google Scholar 

  40. Fertig, H. & Brey, L. Luttinger liquid at the edge of undoped graphene in a strong magnetic field. Phys. Rev. Lett. 97, 116805 (2006).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

The authors acknowledge financial support from the Department of Science and Technology, Government of India. A.A. acknowledges support from CSIR, India, through a senior research fellowship. S.S. acknowledges support from the National Science Foundation (DMR-1508680).

Author information

Authors and Affiliations

Authors

Contributions

A.K. and A.G. conceived and designed the experiments. A.K., T.P.S. and S.B. performed the experiments. A.K., T.P.S., S.B., A.A., T.B., H.R.K., M.J., V.B.S. and A.G. analysed the data. A.A., T.B., S.K.S., H.R.K., M.J. and V.B.S. carried out theoretical modelling and calculations. T.P.S., M.J., V.B.S. and A.G. co-wrote the paper.

Corresponding authors

Correspondence to Amogh Kinikar, T. Phanindra Sai or Arindam Ghosh.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 1246 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kinikar, A., Phanindra Sai, T., Bhattacharyya, S. et al. Quantized edge modes in atomic-scale point contacts in graphene. Nature Nanotech 12, 564–568 (2017). https://doi.org/10.1038/nnano.2017.24

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nnano.2017.24

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing