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 shell structure in sodium nanowires

Abstract

The quantum states of a system of particles in a finite spatial domain in general consist of a set of discrete energy eigenvalues; these are usually grouped into bunches of degenerate or close-lying levels1, called shells. In fermionic systems, this gives rise to a local minimum in the total energy when all the states of a given shell are occupied. In particular, the closed-shell electronic configuration of the noble gases produces their exceptional stability. Shell effects have previously been observed for protons and neutrons in nuclei, and for clusters of metal atoms2,3,4. Here we report the observation of shell effects in an open system—a sodium metal nanowire connecting two bulk sodium metal electrodes, which are progressively pulled apart. We measure oscillations in the statistical distribution of conductance values, for contact cross-sections containing up to a hundred atoms or more. The period follows the law expected from shell-closure effects, similar to the abundance peaks at ‘magic’ numbers of atoms in metal clusters3,4.

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

Access options

Buy this article

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

Figure 1: Schematic view of the MCB technique for alkali metals7.
Figure 2: Temperature evolution of sodium histograms in the range from 0 to 20 G 0.
Figure 3: Conductance histograms for sodium, showing evidence for shell structure.

Similar content being viewed by others

References

  1. Balian, R. & Bloch, C. Distribution of eigenfrequencies for the wave equation in a finite domain: III. Eigenfrequency density oscillations. Ann. Phys. (NY) 69, 76–160 (1972).

    Article  ADS  MathSciNet  Google Scholar 

  2. Bohr, å & Mottelson, B. R. Nuclear StructureVol. II (Benjamin, Reading, Massachusetts, (1975).

    MATH  Google Scholar 

  3. de Heer, W. A. The physics of simple metal clusters: experimental aspects and simple models. Rev. Mod. Phys. 65, 611–676 (1993).

    Article  ADS  CAS  Google Scholar 

  4. Brack, M. The physics of simple metal clusters: self-consistent jellium model and semi-classical approaches. Rev. Mod. Phys. 65, 677–732 (1993).

    Article  ADS  CAS  Google Scholar 

  5. Agraı¨t, N., Rodrigo, J. G. & Vieira, S. Conductance steps and quantization in atomic-size contacts. Phys. Rev. B 47, 12345–12348 (1993).

    Article  ADS  Google Scholar 

  6. Muller, C. J., van Ruitenbeek, J. M. & de Jongh, L. J. Experimental observation of the transition from weak link to tunnel junction. Physica C 191, 485–504 (1992).

    Article  ADS  Google Scholar 

  7. Krans, J. M. et al. The signature of conductance quantization in metallic point contacts. Nature 375, 767–769 (1995).

    Article  ADS  CAS  Google Scholar 

  8. Torres, J. A., Pascual, J. I. & Sáenz, J. J. Theory of conduction through narrow constrictions in a three-dimensional electron gas. Phys. Rev. B 49, 16581–16584 (1994).

    Article  ADS  CAS  Google Scholar 

  9. Knight, W. D. et al. Electronic shell structure and abundances of sodium clusters. Phys. Rev. Lett. 52, 2141–2143 (1984).

    Article  ADS  CAS  Google Scholar 

  10. Martin, T. P. et al. Observation of electronic shells and shells of atoms in large Na clusters. Chem. Phys. Lett. 172, 209–213 (1990).

    Article  ADS  CAS  Google Scholar 

  11. Martin, T. P. et al. Electronic shell structure of laser-warmed Na clusters. Chem. Phys. Lett. 186, 53–57 (1991).

    Article  ADS  CAS  Google Scholar 

  12. Bjørnholm, S. et al. Mean-field quantization of several hundred electrons in sodium metal clusters. Phys. Rev. Lett. 65, 1627–1630 (1990).

    Article  ADS  Google Scholar 

  13. Pedersen, J. et al. Observation of quantum supershells in clusters of sodium atoms. Nature 353, 733–735 (1991).

    Article  ADS  CAS  Google Scholar 

  14. Stafford, C. A., Baeriswyl, D. & Bürki, J. Jellium model of metallic nanocohesion. Phys. Rev. Lett. 79, 2863–2866 (1997).

    Article  ADS  CAS  Google Scholar 

  15. Kassubek, F., Stafford, C. A. & Grabert, H. Force, charge, and conductance of an ideal metallic nanowire. Phys. Rev. B 59, 7560–7574 (1999).

    Article  ADS  CAS  Google Scholar 

  16. van Ruitenbeek, J. M., Devoret, M. H., Esteve, D. & Urbina, C. Conductance quantization in metals: The influence of subband formation on the relative stability of specific contact diameters. Phys. Rev. B 56, 12566–12572 (1997).

    Article  ADS  CAS  Google Scholar 

  17. Yannouleas, C. & Landman, U. On mesoscopic forces and quantized conductance in model metallic nanowires. J. Phys. Chem. B 101, 5780–5783 (1997).

    Article  CAS  Google Scholar 

  18. Yannouleas, C., Bogachek, E. N. & Landman, U. Energetics, forces, and quantized conductance in jellium-modeled metallic nanowires. Phys. Rev. B 57, 4872–4882 (1998).

    Article  ADS  CAS  Google Scholar 

  19. Höppler, C. & Zwerger, W. Quantum fluctuations in the cohesive force of metallic nanowires. Phys. Rev. B 59, R7849–R7851 (1999).

    Article  ADS  Google Scholar 

  20. Ludoph, B. et al. Evidence for saturation of channel transmission from conductance fluctuations in atomic-size point contacts. Phys. Rev. Lett. 82, 1530–1533 (1999).

    Article  ADS  CAS  Google Scholar 

  21. Untiedt, C. et al. Fabrication and characterization of metallic nanowires. Phys. Rev. B 56, 2154–2160 (1997).

    Article  ADS  CAS  Google Scholar 

  22. Gai, Z. et al. Spontaneous breaking of nanowires between a STM tip and the Pb(110) surface. Phys. Rev. B 58, 2185–2190 (1998).

    Article  ADS  CAS  Google Scholar 

Download references

Acknowledgements

We thank L. J. de Jongh for his continuous support.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to J. M. van Ruitenbeek.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yanson, A., Yanson, I. & van Ruitenbeek, J. Observation of shell structure in sodium nanowires. Nature 400, 144–146 (1999). https://doi.org/10.1038/22074

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/22074

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

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