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:

Observation of Aubry-type transition in finite atom chains via friction

Nature Materials volume 15, pages 717–721 (2016)Cite this article

Subjects

Abstract

The highly nonlinear many-body physics of a chain of mutually interacting atoms in contact with a periodic substrate gives rise to complex static and dynamical phenomena, such as structural phase transitions and friction. In the limit of an infinite chain incommensurate with the substrate, Aubry predicted a transition with increasing substrate potential, from the chain’s intrinsic arrangement free to slide on the substrate, to a pinned arrangement favouring the substrate pattern1. So far, the Aubry transition has not been observed. Here, using spatially resolved position and friction measurements of cold trapped ions in an optical lattice2,3, we observed a finite version of the Aubry transition and the onset of its hallmark fractal atomic arrangement. Notably, the observed critical lattice depth for few-ion chains agrees well with the infinite-chain prediction. Our results elucidate the connection between competing ordering patterns and superlubricity in nanocontacts—the elementary building blocks of friction.

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

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

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

Figure 1: A nanocontact, the ion-lattice system, the Frenkel–Kontorova–Tomlinson (FKT) model and the Aubry transition.
Figure 2: Observation of primary and secondary position gap formation in a mismatched two-ion chain.
Figure 3: Observation of superlubricity breaking for matched and mismatched ion chains.
Figure 4: Aubry transition in finite mismatched ion chains.

Similar content being viewed by others

References

  1. Aubry, S. The twist map, the extended Frenkel–Kontorova model and the Devil’s staircase. Physica D 7, 240–258 (1983).

    Article  Google Scholar 

  2. Bylinskii, A., Gangloff, D. & Vuletić, V. Tuning friction atom-by-atom in an ion-crystal simulator. Science 348, 1115–1119 (2015).

    Article  CAS  Google Scholar 

  3. Gangloff, D., Bylinskii, A., Counts, I., Jhe, W. & Vuletić, V. Velocity tuning of friction with two trapped atoms. Nature Phys. 11, 915–919 (2015).

    Article  CAS  Google Scholar 

  4. Braun, O. M. & Kivshar, Y. S. The Frenkel–Kontorova Model: Concepts, Methods, and Applications (Springer, 2004).

    Book  Google Scholar 

  5. Biham, O. & Mukamel, D. Global universality in the Frenkel–Kontorova model. Phys. Rev. A 29, 5326–5335 (1989).

    Article  Google Scholar 

  6. Sharma, S., Bergersen, B. & Joos, B. Aubry transition in a finite modulated chain. Phys. Rev. B 39, 6335–6340 (1984).

    Article  Google Scholar 

  7. Braiman, Y., Baumgarten, J., Jortner, J. & Klafter, J. Symmetry-breaking transition in finite Frenkel–Kontorova chains. Phys. Rev. Lett. 65, 2398–2401 (1990).

    Article  CAS  Google Scholar 

  8. Mo, Y., Turner, K. T. & Szlufarska, I. Friction laws at the nanoscale. Nature 457, 1116–1119 (2009).

    Article  CAS  Google Scholar 

  9. Ward, A. et al. Solid friction between soft filaments. Nature Mater. 14, 583–588 (2015).

    Article  CAS  Google Scholar 

  10. Grüner, G. The dynamics of charge-density waves. Rev. Mod. Phys. 60, 1129–1181 (1988).

    Article  Google Scholar 

  11. Braun, O. & Naumovets, A. Nanotribology: microscopic mechanisms of friction. Surf. Sci. Rep. 60, 79–158 (2006).

    Article  CAS  Google Scholar 

  12. Bormuth, V., Varga, V., Howard, J. & Schäffer, E. Protein friction limits diffusive and directed movements of kinesin motors on microtubules. Science 325, 870–873 (2009).

    Article  CAS  Google Scholar 

  13. Shinjo, K. & Hirano, M. Dynamics of friction: superlubric state. Surf. Sci. 283, 473–478 (1993).

    Article  CAS  Google Scholar 

  14. Vanossi, A., Manini, N., Urbakh, M., Zapperi, S. & Tosatti, E. Colloquium: modeling friction: from nanoscale to mesoscale. Rev. Mod. Phys. 85, 529–552 (2013).

    Article  CAS  Google Scholar 

  15. Krylov, S. Y. & Frenken, J. W. M. The physics of atomic-scale friction: basic considerations and open questions. Phys. Status Solidi B 251, 711–736 (2014).

    Article  CAS  Google Scholar 

  16. Szlufarska, I., Chandross, M. & Carpick, R. W. Recent advances in single-asperity nanotribology. J. Phys. D 41, 123001 (2008).

    Article  Google Scholar 

  17. Urbakh, M. & Meyer, E. Nanotribology: the renaissance of friction. Nature Mater. 9, 8–10 (2010).

    Article  CAS  Google Scholar 

  18. Bohlein, T., Mikhael, J. & Bechinger, C. Observation of kinks and antikinks in colloidal monolayers driven across ordered surfaces. Nature Mater. 11, 126–130 (2012).

    Article  CAS  Google Scholar 

  19. Socoliuc, A., Bennewitz, R., Gnecco, E. & Meyer, E. Transition from stick–slip to continuous sliding in atomic friction: entering a new regime of ultralow friction. Phys. Rev. Lett. 92, 134301 (2004).

    Article  CAS  Google Scholar 

  20. Dienwiebel, M. et al. Superlubricity of graphite. Phys. Rev. Lett. 92, 126101 (2004).

    Article  Google Scholar 

  21. García-Mata, I., Zhirov, O. V. & Shepelyansky, D. L. Frenkel–Kontorova model with cold trapped ions. Eur. Phys. J. D 41, 325–330 (2006).

    Google Scholar 

  22. Benassi, A., Vanossi, A. & Tosatti, E. Nanofriction in cold ion traps. Nature Commun. 2, 236 (2011).

    Article  CAS  Google Scholar 

  23. Pruttivarasin, T., Ramm, M., Talukdar, I., Kreuter, A. & Häffner, H. Trapped ions in optical lattices for probing oscillator chain models. New J. Phys. 13, 075012 (2011).

    Article  Google Scholar 

  24. Weiss, M. & Elmer, F.-J. Dry friction in the Frenkel–Kontorova–Tomlinson model: static properties. Phys. Rev. B 53, 7539–7549 (1996).

    Article  CAS  Google Scholar 

  25. Weiss, M. & Elmer, F.-J. Dry friction in the Frenkel–Kontorova–Tomlinson Model: dynamical properties. Z. Phys. B 69, 55–69 (1997).

    Article  Google Scholar 

  26. Karpa, L., Bylinskii, A., Gangloff, D., Cetina, M. & Vuletić, V. Suppression of ion transport due to long-lived subwavelength localization by an optical lattice. Phys. Rev. Lett. 111, 163002 (2013).

    Article  Google Scholar 

  27. Cetina, M. et al. One-dimensional array of ion chains coupled to an optical cavity. New J. Phys. 15, 053001 (2013).

    Article  Google Scholar 

  28. Igarashi, M., Natori, A. & Nakamura, J. Size effects in friction of multiatomic sliding contacts. Phys. Rev. B 78, 165427 (2008).

    Article  Google Scholar 

  29. Coppersmith, S. N. & Fisher, D. Pinning transition of the discrete sine-Gordon equation. Phys. Rev. B 28, 2566–2581 (1983).

    Article  Google Scholar 

  30. Fogarty, T. et al. Nanofriction in cavity quantum electrodynamics. Phys. Rev. Lett. 115, 233602 (2015).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

We thank W. Jhe for helpful discussions. A.B. and D.G. acknowledge scholarship support from NSERC. This work was supported by the NSF.

Author information

Author notes

  1. Alexei Bylinskii

    Present address: Present address: Department of Physics and Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02139, USA.,

  2. Alexei Bylinskii and Dorian Gangloff: These authors contributed equally to this work.

Authors and Affiliations

  1. Department of Physics, MIT-Harvard Center for Ultracold Atoms and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

    Alexei Bylinskii, Dorian Gangloff, Ian Counts & Vladan Vuletić

Authors
  1. Alexei Bylinskii
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dorian Gangloff
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ian Counts
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Vladan Vuletić
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

A.B., D.G. and V.V. designed the experiments. D.G., A.B. and I.C. collected and analysed data. All authors discussed the results and contributed to the manuscript preparation.

Corresponding author

Correspondence to Vladan Vuletić.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 311 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bylinskii, A., Gangloff, D., Counts, I. et al. Observation of Aubry-type transition in finite atom chains via friction. Nature Mater 15, 717–721 (2016). https://doi.org/10.1038/nmat4601

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nmat4601

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