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.

  • Letter
  • Published:

Superballistic flow of viscous electron fluid through graphene constrictions

Nature Physics volume 13, pages 1182–1185 (2017)Cite this article

Subjects

Abstract

Electron–electron (e–e) collisions can impact transport in a variety of surprising and sometimes counterintuitive ways1,2,3,4,5,6. Despite strong interest, experiments on the subject proved challenging because of the simultaneous presence of different scattering mechanisms that suppress or obscure consequences of e–e scattering7,8,9,10,11. Only recently, sufficiently clean electron systems with transport dominated by e–e collisions have become available, showing behaviour characteristic of highly viscous fluids12,13,14. Here we study electron transport through graphene constrictions and show that their conductance below 150 K increases with increasing temperature, in stark contrast to the metallic character of doped graphene15. Notably, the measured conductance exceeds the maximum conductance possible for free electrons16,17. This anomalous behaviour is attributed to collective movement of interacting electrons, which ‘shields’ individual carriers from momentum loss at sample boundaries18,19. The measurements allow us to identify the conductance contribution arising due to electron viscosity and determine its temperature dependence. Besides fundamental interest, our work shows that viscous effects can facilitate high-mobility transport at elevated temperatures, a potentially useful behaviour for designing graphene-based devices.

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

Access options

Buy this article

  • Purchase on SpringerLink
  • Instant access to the full article PDF.

USD 39.95

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

Figure 1: Electron flow through graphene constrictions.
Figure 2: Transition from metallic to insulating behaviour in constrictions of different widths.
Figure 3: Quantifying e–e interactions in graphene.

Similar content being viewed by others

References

  1. Gurzhi, R. N. Minimum of resistance in impurity-fee conductors. Sov. Phys. JETP 17, 521–522 (1963).

    Google Scholar 

  2. Gurzhi, R. N. Hydrodynamic effects in solids at low temperature. Sov. Phys. Usp. 11, 255–270 (1968).

    Article  ADS  Google Scholar 

  3. Govorov, A. O. & Heremans, J. J. Hydrodynamic effects in interacting Fermi electron jets. Phys. Rev. Lett. 92, 026803 (2004).

    Article  ADS  Google Scholar 

  4. Müller, M., Schmalian, J. & Fritz, L. Graphene: a nearly perfect fluid. Phys. Rev. Lett. 103, 025301 (2009).

    Article  ADS  Google Scholar 

  5. Mendoza, M., Herrmann, H. J. & Succi, S. Preturbulent regimes in graphene flow. Phys. Rev. Lett. 106, 156601 (2011).

    Article  ADS  Google Scholar 

  6. Forcella, D., Zaanen, J., Valentinis, D. & van der Marel, D. Electromagnetic properties of viscous charged fluids. Phys. Rev. B 90, 035143 (2014).

    Article  ADS  Google Scholar 

  7. Yu, Z. Z. et al. Negative temperature derivative of resistivity in thin potassium samples: the Gurzhi Effect? Phys. Rev. Lett. 52, 368–371 (1984).

    Article  ADS  Google Scholar 

  8. de Jong, M. J. M. & Molenkamp, L. W. Hydrodynamic electron flow in high-mobility wires. Phys. Rev. B 51, 13389–13402 (1995).

    Article  ADS  Google Scholar 

  9. Renard, V. et al. Boundary-mediated electron–electron interactions in quantum point contacts. Phys. Rev. Lett. 100, 186801 (2008).

    Article  ADS  Google Scholar 

  10. Nagaev, K. E. & Kostyuchenko, T. V. Electron–electron scattering and magnetoresistance of ballistic microcontacts. Phys. Rev. B 81, 125316 (2010).

    Article  ADS  Google Scholar 

  11. Melnikov, M. Y. et al. Influence of e–e scattering on the temperature dependence of the resistance of a classical ballistic point contact in a two-dimensional electron system. Phys. Rev. B 86, 075425 (2012).

    Article  ADS  Google Scholar 

  12. Bandurin, D. A. et al. Negative local resistance caused by viscous electron backflow in graphene. Science 351, 1055–1058 (2016).

    Article  ADS  Google Scholar 

  13. Crossno, J. et al. Observation of the Dirac fluid and the breakdown of the Wiedemann–Franz law in graphene. Science 351, 1058–1061 (2016).

    Article  ADS  Google Scholar 

  14. Moll, P. J. W., Kushwaha, P., Nandi, N., Schmidt, B. & Mackenzie, A. P. Evidence for hydrodynamic electron flow in PdCoO2 . Science 351, 1061–1064 (2016).

    Article  ADS  Google Scholar 

  15. 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).

    Article  ADS  Google Scholar 

  16. Sharvin, Y. V. A possible method for studying Fermi surfaces. Sov. Phys. JETP 21, 655–656 (1965).

    ADS  Google Scholar 

  17. Beenakker, C. W. J. & van Houten, H. Quantum transport in semiconductor nanostructures. Solid State Phys. 44, 1–228 (1991).

    Article  Google Scholar 

  18. Guo, H., Ilseven, E., Falkovich, G. & Levitov, L. Higher-than-ballistic conduction of viscous electron flows. Proc. Natl Acad. Sci. USA 114, 3068–3073 (2017).

    Article  ADS  Google Scholar 

  19. Guo, H., Ilseven, E., Falkovich, G. & Levitov, L. Stokes paradox, back reflections and interaction-enhanced conduction. Preprint at http://arxiv.org/abs/1612.09239 (2016).

  20. Mayorov, A. S. et al. Micrometer-scale ballistic transport in encapsulated graphene at room temperature. Nano Lett. 11, 2396–2399 (2011).

    Article  ADS  Google Scholar 

  21. Wang, L. et al. One-dimensional electrical contact to a two-dimensional material. Science 342, 614–617 (2013).

    Article  ADS  Google Scholar 

  22. Torre, I., Tomadin, A., Geim, A. K. & Polini, M. Nonlocal transport and the hydrodynamic shear viscosity in graphene. Phys. Rev. B 92, 165433 (2015).

    Article  ADS  Google Scholar 

  23. Levitov, L. & Falkovich, G. Electron viscosity, current vortices and negative nonlocal resistance in graphene. Nat. Phys. 12, 672–676 (2016).

    Article  Google Scholar 

  24. Knudsen, M. Die Gesetze der Molekularströmung und der inneren Reibungsströmung der Gase durch Röhren (The laws of molecular flow and of inner frictional flow of gases through tubes). Ann. Phys. 28, 75–130 (1909).

    Article  Google Scholar 

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

    Article  Google Scholar 

  26. Terrés, B. et al. Size quantization of Dirac fermions in graphene constrictions. Nat. Commun. 7, 11528 (2016).

    Article  ADS  Google Scholar 

  27. Kotov, V. N., Uchoa, B., Pereira, V. M., Guinea, F. & Castro Neto, A. H. Electron–electron interactions in graphene: Current status and perspectives. Rev. Mod. Phys. 84, 1067–1125 (2012).

    Article  ADS  Google Scholar 

  28. de Jong, M. J. M. Transition from Sharvin to Drude resistance in high-mobility wires. Phys. Rev. B 49, 7778–7781 (1994).

    Article  ADS  Google Scholar 

  29. Principi, A., Vignale, G., Carrega, M. & Polini, M. Bulk and shear viscosities of the 2D electron liquid in a doped graphene sheet. Phys. Rev. B 93, 125410 (2016).

    Article  ADS  Google Scholar 

  30. Polini, M. & Vignale, G. The quasiparticle lifetime in a doped graphene sheet. Preprint at http://arxiv.org/abs/1404.5728 (2014).

Download references

Acknowledgements

This work was supported by Engineering and Physical Sciences Research Council, Graphene Flagship, the Royal Society and Lloyd’s Register Foundation. L.S.L. acknowledges support from the Center for Integrated Quantum Materials under NSF award 1231319, the Center for Excitonics, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Basic Energy Sciences, under award DESC0001088, and MIT-Israel Seed Fund. G.F. acknowledges ISF grant 882 and RSF grant 14-22-00259. A.P. was supported by ERC Advanced Grant FEMTO/NANO and Spinoza Prize. M.P. acknowledges Fondazione Istituto Italiano di Tecnologia and the European Union’s Horizon 2020 programme under grant 696656 ‘GrapheneCore1’. D.A.B. and I.V.G. thank the Marie Curie programme SPINOGRAPH. G.H.A. was supported by EPSRC grant EP/M507969. R.K.K. acknowledges support from Doctoral Training Centre NOWNANO. The authors would like to thank E. Khestanova for the help with AFM measurements.

Author information

Authors and Affiliations

  1. School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK

    R. Krishna Kumar, D. A. Bandurin, M. Ben Shalom, I. V. Grigorieva, M. Polini & A. K. Geim

  2. National Graphene Institute, University of Manchester, Manchester M13 9PL, UK

    R. Krishna Kumar, D. A. Bandurin, Y. Cao, G. H. Auton, M. Ben Shalom & A. K. Geim

  3. Department of Physics, University of Lancaster, Lancaster LA1 4YW, UK

    R. Krishna Kumar & L. A. Ponomarenko

  4. NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, 56126 Pisa, Italy

    F. M. D. Pellegrino

  5. Radboud University, Institute for Molecules and Materials, 6525 AJ Nijmegen, The Netherlands

    A. Principi

  6. Massachusetts Institute of Technology, Cambridge, Massachusetts, 02139, USA

    H. Guo & L. S. Levitov

  7. Department of Physics, Weizmann Institute of Science, Rehovot, 76100, Israel

    G. Falkovich

  8. Institute for Information Transmission Problems, Moscow 127994, Russia

    G. Falkovich

  9. National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan

    K. Watanabe & T. Taniguchi

  10. Istituto Italiano di Tecnologia, Graphene Labs, Via Morego 30, 16163 Genova, Italy

    M. Polini

Authors
  1. R. Krishna Kumar
    View author publications

    Search author on:PubMed Google Scholar

  2. D. A. Bandurin
    View author publications

    Search author on:PubMed Google Scholar

  3. F. M. D. Pellegrino
    View author publications

    Search author on:PubMed Google Scholar

  4. Y. Cao
    View author publications

    Search author on:PubMed Google Scholar

  5. A. Principi
    View author publications

    Search author on:PubMed Google Scholar

  6. H. Guo
    View author publications

    Search author on:PubMed Google Scholar

  7. G. H. Auton
    View author publications

    Search author on:PubMed Google Scholar

  8. M. Ben Shalom
    View author publications

    Search author on:PubMed Google Scholar

  9. L. A. Ponomarenko
    View author publications

    Search author on:PubMed Google Scholar

  10. G. Falkovich
    View author publications

    Search author on:PubMed Google Scholar

  11. K. Watanabe
    View author publications

    Search author on:PubMed Google Scholar

  12. T. Taniguchi
    View author publications

    Search author on:PubMed Google Scholar

  13. I. V. Grigorieva
    View author publications

    Search author on:PubMed Google Scholar

  14. L. S. Levitov
    View author publications

    Search author on:PubMed Google Scholar

  15. M. Polini
    View author publications

    Search author on:PubMed Google Scholar

  16. A. K. Geim
    View author publications

    Search author on:PubMed Google Scholar

Contributions

A.K.G., L.S.L. and M.P. designed and supervised the project. Y.C., G.H.A. and M.B.S. fabricated the studied devices. T.T. and K.W. provided quality boron-nitride crystals. Transport measurements and data analysis were carried out by R.K.K. and D.A.B. Theory analysis was done by F.M.D.P., A.P., H.G., G.F., L.S.L. and M.P. R.K.K., D.A.B., L.S.L., M.P. and A.K.G. wrote the manuscript. L.S.L. wrote Supplementary Section 4. A.P. and M.P. wrote Supplementary Sections 6 and 8. L.A.P. and I.V.G. provided experimental support and contributed to writing the manuscript. All authors contributed to discussions.

Corresponding author

Correspondence to A. K. Geim.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information (download PDF )

Supplementary information (PDF 810 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Krishna Kumar, R., Bandurin, D., Pellegrino, F. et al. Superballistic flow of viscous electron fluid through graphene constrictions. Nature Phys 13, 1182–1185 (2017). https://doi.org/10.1038/nphys4240

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue date:

  • DOI: https://doi.org/10.1038/nphys4240

This article is cited by

Search

Advanced 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