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.

Mechanically controlled quantum interference in graphene break junctions

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 options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Fig. 1: Nanofabrication of graphene MCBJs.
Fig. 2: Electromechanical measurements reveal conductance oscillations.
Fig. 3: Analysis of the oscillation periodicities.
Fig. 4: DFT and tight-binding calculations of sliding graphene bilayers.

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.

References

  1. 1.

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

    Article  Google Scholar 

  2. 2.

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

    CAS  Article  Google Scholar 

  3. 3.

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

    CAS  Article  Google Scholar 

  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).

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  6. 6.

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

    CAS  Article  Google Scholar 

  7. 7.

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

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  9. 9.

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

    CAS  Article  Google Scholar 

  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).

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  12. 12.

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

    CAS  Article  Google Scholar 

  13. 13.

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

    CAS  Article  Google Scholar 

  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).

    CAS  Article  Google Scholar 

  15. 15.

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

    CAS  Article  Google Scholar 

  16. 16.

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

    CAS  Article  Google Scholar 

  17. 17.

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

    CAS  Article  Google Scholar 

  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).

    CAS  Article  Google Scholar 

  19. 19.

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

    CAS  Article  Google Scholar 

  20. 20.

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

    CAS  Article  Google Scholar 

  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).

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  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).

    CAS  Article  Google Scholar 

  24. 24.

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

    CAS  Article  Google Scholar 

  25. 25.

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

    CAS  Article  Google Scholar 

  26. 26.

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

    Article  Google Scholar 

  27. 27.

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

    CAS  Article  Google Scholar 

  28. 28.

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

    CAS  Article  Google Scholar 

  29. 29.

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

    Article  Google Scholar 

  30. 30.

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

    CAS  Article  Google Scholar 

  31. 31.

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

    Article  Google Scholar 

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

Authors

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.

Corresponding authors

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

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

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

Supplementary information

Supplementary Information

Supplementary Figures 1–13, Supplementary Tables 1–2

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Caneva, S., Gehring, P., García-Suárez, V.M. et al. Mechanically controlled quantum interference in graphene break junctions. Nature Nanotech 13, 1126–1131 (2018). https://doi.org/10.1038/s41565-018-0258-0

Download citation

Further reading

Search

Quick links

Find nanotechnology articles, nanomaterial data and patents all in one place. Visit Nano by Nature Research