Abstract

The ability to detect and distinguish quantum interference signatures is important for both fundamental research and for the realization of devices such as electron resonators1, interferometers2 and interference-based spin filters3. Consistent with the principles of subwavelength optics, the wave nature of electrons can give rise to various types of interference effects4, such as Fabry–Pérot resonances5, Fano resonances6 and the Aharonov–Bohm effect7. Quantum interference conductance oscillations8 have, indeed, been predicted for multiwall carbon nanotube shuttles and telescopes, and arise from atomic-scale displacements between the inner and outer tubes9,10. Previous theoretical work on graphene bilayers indicates that these systems may display similar interference features as a function of the relative position of the two sheets11,12. Experimental verification is, however, still lacking. Graphene nanoconstrictions represent an ideal model system to study quantum transport phenomena13,14,15 due to the electronic coherence16 and the transverse confinement of the carriers17. Here, we demonstrate the fabrication of bowtie-shaped nanoconstrictions with mechanically controlled break junctions made from a single layer of graphene. Their electrical conductance displays pronounced oscillations at room temperature, with amplitudes that modulate over an order of magnitude as a function of subnanometre displacements. Surprisingly, the oscillations exhibit a period larger than the graphene lattice constant. Charge-transport calculations show that the periodicity originates from a combination of the quantum interference and lattice commensuration effects of two graphene layers that slide across each other. Our results provide direct experimental observation of a Fabry–Pérot-like interference of electron waves that are partially reflected and/or transmitted at the edges of the graphene bilayer overlap region.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.

Additional information

Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

References

  1. 1.

    Liang, W. et al. Fabry–Pérot interference in a nanotube electron waveguide. Nature 411, 665–669 (2010).

  2. 2.

    Ji, Y. et al. An electronic Mach–Zehnder interferometer. Nature 422, 415–418 (2003).

  3. 3.

    Lundeberg, M. B. & Folk, J. A. Spin-resolved quantum interference in graphene. Nat. Phys. 5, 894–897 (2009).

  4. 4.

    Darancet, P., Olevano, V. & Mayou, D. Coherent electronic transport through graphene constrictions: subwavelength regime and optical analogy. Phys. Rev. Lett. 102, 2–5 (2009).

  5. 5.

    Shytov, A. V., Rudner, M. S. & Levitov, L. S. Klein backscattering and Fabry–Pérot interference in graphene heterojunctions. Phys. Rev. Lett. 101, 156804 (2008).

  6. 6.

    Gehring, P. et al. Quantum interference in graphene nanoconstrictions. Nano Lett. 16, 4210–4216 (2016).

  7. 7.

    Russo, S. et al. Observation of Aharonov–Bohm conductance oscillations in a graphene ring. Phys. Rev. B 77, 1–5 (2008).

  8. 8.

    Grace, I. M., Bailey, S. W. & Lambert, C. J. Electron transport in carbon nanotube shuttles and telescopes. Phys. Rev. B 70, 153405 (2004).

  9. 9.

    Jiang, H. et al. Carbon nanotube electronic displacement encoder with sub-nanometer resolution. J. Comput. Theor. Nanosci. 4, 574–577 (2007).

  10. 10.

    Tunney, M. A. & Cooper, N. R. Effects of disorder and momentum relaxation on the intertube transport of incommensurate carbon nanotube ropes and multiwall nanotubes. Phys. Rev. B 74, 075406 (2006).

  11. 11.

    Popov, A. M. et al. AA stacking, tribological and electronic properties of double-layer graphene with krypton spacer. J. Chem. Phys. 139, 154705 (2013).

  12. 12.

    Poklonski, N. A. et al. Graphene-based nanodynamometer. J. Comput. Theor. Nanosci. 10, 141–146 (2013).

  13. 13.

    Miao, F. et al. Phase-coherent transport in graphene quantum billiards. Science 317, 1530–1533 (2007).

  14. 14.

    Zhang, Y., Tan, Y., Stormer, H. L. & Kim, P. Experimental observation of the quantum Hall effect and Berry’s phase in graphene. Nature 438, 201–204 (2005).

  15. 15.

    Sadeghi, H. et al. Conductance enlargement in picoscale electroburnt graphene nanojunctions. Proc. Natl Acad. Sci. USA 112, 2658–2663 (2015).

  16. 16.

    Berger, C. et al. Electronic confinement and coherence in patterned epitaxial graphene. Science 312, 1191–1197 (2006).

  17. 17.

    Young, A. F. & Kim, P. Quantum interference and Klein tunnelling in graphene heterojunctions. Nat. Phys. 5, 222–226 (2009).

  18. 18.

    Frisenda, R., Janssen, V. A. E. C., Grozema, F. C., van der Zant, H. S. J. & Renaud, N. Mechanically controlled quantum interference in individual π-stacked dimers. Nat. Chem. 8, 1099–1104 (2016).

  19. 19.

    Kinikar, A. et al. Quantized edge modes in atomic-scale contacts in graphene. Nat. Nanotech. 12, 564–568 (2017).

  20. 20.

    Benameur, M. M. et al. Electromechanical oscillations in bilayer graphene. Nat. Commun. 6, 8582 (2015).

  21. 21.

    Simmons, J. G. Generalized formula for the electric tunnel effect between similar electrodes separated by a thin insulating film. J. Appl. Phys. 34, 1793 (1963).

  22. 22.

    González, J. W., Santos, H., Pacheco, M., Chico, L. & Brey, L. Electronic transport through bilayer graphene flakes. Phys. Rev. B 81, 195406 (2010).

  23. 23.

    Zhang, H. et al. Visualizing electrical breakdown and on/off states in electrically switchable suspended graphene break junctions. Nano Lett. 12, 1772–1775 (2012).

  24. 24.

    Sarwat, S. G. et al. Scaling limits of graphene nanoelectrodes. Nano Lett. 17, 3688–3693 (2017).

  25. 25.

    Bellunato, A. et al. Dynamic tunneling junctions at the atomic intersection of two twisted graphene edges. Nano Lett. 18, 2505–2510 (2018).

  26. 26.

    Isacsson, A. Nanomechanical displacement detection using coherent transport in graphene nanoribbon resonators. Phys. Rev. B 84, 125452 (2011).

  27. 27.

    Heerema, S. J. & Dekker, C. Graphene nanodevices for DNA sequencing. Nat. Nanotech. 11, 127–136 (2016).

  28. 28.

    Di Ventra, M. & Taniguchi, M. Decoding DNA, RNA and peptides with quantum tunnelling. Nat. Nanotech. 11, 117–126 (2016).

  29. 29.

    Rickhaus, P. et al. Ballistic interferences in suspended graphene. Nat. Commun. 4, 2342 (2013).

  30. 30.

    Soler, M. J. et al. The SIESTA method for ab initio order-N materials simulation. J. Phys. Condens. Matter 14, 2745 (2002).

  31. 31.

    Ferrer, J. et al. GOLLUM: a next-generation simulation tool for electron, thermal and spin transport. New J. Phys. 16, 093029 (2014).

Download references

Acknowledgements

S.C. acknowledges a Marie Skłodowska-Curie Individual Fellowship under grant BioGraphING (ID 798851) and P.G. acknowledges a Marie Skłodowska-Curie Individual Fellowship under grant TherSpinMol (ID 748642) from the European Union’s Horizon 2020 research and innovation programme. This work was supported by the Graphene Flagship (a European Union’s Horizon 2020 research and innovation programme under grant agreement no. 649953), the Marie Curie ITN MOLESCO and an ERC advanced grant (Mols@Mols No. 240299). The research by V.M.G.-S., A.G-F. and J.F. was funded by the project FIS2015-63918-R from the Spanish government.

Author information

Affiliations

  1. Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands

    • Sabina Caneva
    • , Pascal Gehring
    • , Davide Stefani
    • , Ignacio J. Olavarria-Contreras
    • , Cees Dekker
    •  & Herre S. J. van der Zant
  2. Departamento de Física, Universidad de Oviedo, Oviedo, Spain

    • Víctor M. García-Suárez
    • , Amador García-Fuente
    •  & Jaime Ferrer
  3. Nanomaterials and Nanotechnology Research Center, CSIC – Universidad de Oviedo, Oviedo, Spain

    • Víctor M. García-Suárez
    •  & Jaime Ferrer

Authors

  1. Search for Sabina Caneva in:

  2. Search for Pascal Gehring in:

  3. Search for Víctor M. García-Suárez in:

  4. Search for Amador García-Fuente in:

  5. Search for Davide Stefani in:

  6. Search for Ignacio J. Olavarria-Contreras in:

  7. Search for Jaime Ferrer in:

  8. Search for Cees Dekker in:

  9. Search for Herre S. J. van der Zant in:

Contributions

S.C., H.S.J.Z. and C.D. conceived the idea and designed the experiments. S.C. developed the nanofabrication protocol. S.C., I.J.O.-C., D.S. and P.G. performed the break junction experiments. P.G. and S.C. performed the graphene gating measurements. P.G. designed and implemented the cross-correlation method and performed the I–V data analysis. J.F. supervised the theoretical research work. V.M.G.-S. and J.F. conceived the simulations. A.G.-F. and V.M.G.-S. carried out the DFT calculations. V.M.G.-S. and J.F. carried out the tight-binding calculations. J.F. developed the algebraic analysis of the charge transport model and of the interference conditions. All the authors participated in discussions and co-wrote the paper.

Competing interests

The authors declare no competing interests.

Corresponding authors

Correspondence to Jaime Ferrer or Herre S. J. van der Zant.

Supplementary information

  1. Supplementary Information

    Supplementary Figures 1–13, Supplementary Tables 1–2

About this article

Publication history

Received

Accepted

Published

DOI

https://doi.org/10.1038/s41565-018-0258-0