Article | Published:

Quantized edge modes in atomic-scale point contacts in graphene

Nature Nanotechnology volume 12, pages 564568 (2017) | Download Citation

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.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

References

  1. 1.

    , , & Energy band-gap engineering of graphene nanoribbons. Phys. Rev. Lett. 98, 206805 (2007).

  2. 2.

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

  3. 3.

    , , & Quantum dot behavior in graphene nanoconstrictions. Nano Lett. 9, 416–421 (2009).

  4. 4.

    , , & Electrical observation of subband formation in graphene nanoribbons. Phys. Rev. B 78, 161409 (2008).

  5. 5.

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

  6. 6.

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

  7. 7.

    , , , & Graphene edges: a review of their fabrication and characterization. Nanoscale 3, 86–95 (2011).

  8. 8.

    , & Conductance quantization and transport gaps in disordered graphene nanoribbons. Phys. Rev. B 79, 075407 (2009).

  9. 9.

    , , & Graphene nano-ribbon electronics. Physica E 40, 228–232 (2007).

  10. 10.

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

  11. 11.

    , , , & Narrow graphene nanoribbons from carbon nanotubes. Nature 458, 877–880 (2009).

  12. 12.

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

  13. 13.

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

  14. 14.

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

  15. 15.

    , , , & Characterizing wave functions in graphene nanodevices: electronic transport through ultrashort graphene constrictions on a boron nitride substrate. Phys. Rev. B 90, 115405 (2014).

  16. 16.

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

  17. 17.

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

  18. 18.

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

  19. 19.

    , , & Edge state in graphene ribbons: nanometer size effect and edge shape dependence. Phys. Rev. B 54, 17954 (1996).

  20. 20.

    & Conductance quantization in strongly disordered graphene ribbons. Phys. Rev. B 80, 201407 (2009).

  21. 21.

    , , & Topological origin of subgap conductance in insulating bilayer graphene. Nat. Phys. 7, 38–42 (2011).

  22. 22.

    , , & Tearing graphene sheets from adhesive substrates produces tapered nanoribbons. Small 6, 1108–1116 (2010).

  23. 23.

    , , & Valley-Hall kink and edge states in multilayer graphene. Phys. Rev. B 84, 075418 (2011).

  24. 24.

    , & Perfectly conducting channel and universality crossover in disordered graphene nanoribbons. Phys. Rev. Lett. 99, 036601 (2007).

  25. 25.

    , , , & Localized states at zigzag edges of bilayer graphene. Phys. Rev. Lett. 100, 026802 (2008).

  26. 26.

    , & Unique chemical reactivity of a graphene nanoribbon's zigzag edge. J Chem. Phys. 126, 134701 (2007).

  27. 27.

    , & Self-passivating edge reconstructions of graphene. Phys. Rev. Lett. 101, 115502 (2008).

  28. 28.

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

  29. 29.

    , , & Peculiar localized state at zigzag graphite edge. J. Phys. Soc. Jpn 65, 1920–1923 (1996).

  30. 30.

    , & Half-metallic graphene nanoribbons. Nature 444, 347–349 (2006).

  31. 31.

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

  32. 32.

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

  33. 33.

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

  34. 34.

    , , & Dynamic localization of two-dimensional electrons at mesoscopic length scales. Phys. Rev. B 70, 233309 (2004).

  35. 35.

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

  36. 36.

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

  37. 37.

    , , , & The signature of conductance quantization in metallic point contacts. Nature 375, 767–769 (1995).

  38. 38.

    , , & Carbon nanotube quantum resistors. Science 280, 1744–1746 (1998).

  39. 39.

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

  40. 40.

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

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

Affiliations

  1. Department of Physics, Indian Institute of Science, Bengaluru 560 012, India

    • Amogh Kinikar
    • , T. Phanindra Sai
    • , Semonti Bhattacharyya
    • , Adhip Agarwala
    • , Tathagata Biswas
    • , H. R. Krishnamurthy
    • , Manish Jain
    • , Vijay B. Shenoy
    •  & Arindam Ghosh
  2. Department of Physics, The University of Alabama, Tuscaloosa, Alabama 35487, USA

    • Sanjoy K. Sarker
  3. Centre for Nano Science and Engineering, Indian Institute of Science, Bangalore 560 012, India

    • Arindam Ghosh

Authors

  1. Search for Amogh Kinikar in:

  2. Search for T. Phanindra Sai in:

  3. Search for Semonti Bhattacharyya in:

  4. Search for Adhip Agarwala in:

  5. Search for Tathagata Biswas in:

  6. Search for Sanjoy K. Sarker in:

  7. Search for H. R. Krishnamurthy in:

  8. Search for Manish Jain in:

  9. Search for Vijay B. Shenoy in:

  10. Search for Arindam Ghosh in:

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.

Competing interests

The authors declare no competing financial interests.

Corresponding authors

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

Supplementary information

PDF files

  1. 1.

    Supplementary information

    Supplementary information

About this article

Publication history

Received

Accepted

Published

DOI

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

Further reading