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Aharonov–Bohm oscillations in carbon nanotubes

Nature volume 397, pages 673–675 (1999)Cite this article

Abstract

When electrons pass through a cylindrical electrical conductor aligned in a magnetic field, their wave-like nature manifests itself as a periodic oscillation in the electrical resistance as a function of the enclosed magnetic flux1. This phenomenon reflects the dependence of the phase of the electron wave on the magnetic field, known as the Aharonov–Bohm effect2, which causes a phase difference, and hence interference, between partial waves encircling the conductor in opposite directions. Such oscillations have been observed in micrometre-sized thin-walled metallic cylinders3,4,5 and lithographically fabricated rings6,7,8. Carbon nanotubes9,10 are composed of individual graphene sheets rolled into seamless hollow cylinders with diameters ranging from 1 nm to about 20 nm. They are able to act as conducting molecular wires11,12,13,14,15,16,17,18, making them ideally suited for the investigation of quantum interference at the single-molecule level caused by the Aharonov–Bohm effect. Here we report magnetoresistance measurements on individual multi-walled nanotubes, which display pronounced resistance oscillations as a function of magnetic flux.We find that the oscillations are in good agreement with theoretical predictions for the Aharonov–Bohm effect in a hollow conductor with a diameter equal to that of the outermost shell of the nanotubes. In some nanotubes we also observe shorter-period oscillations, which might result from anisotropic electron currents caused by defects in the nanotube lattice.

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Figure 1: A single multi-walled carbon nanotube electrically contacted with four electrodes.
Figure 2: Magnetoresistance R (B) at five different temperatures T measured for a MWNT in a parallel magnetic field B (solid curves).
Figure 3: As Fig. 2 but for two different temperatures T on another MWNT.

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References

  1. Altshuler, B. L., Aronov, A. G. & Spivak, B. Z. The Aharonov–Bohm effect in disordered conductors. Pis'ma Zh. Eksp. Teor. Fiz. 33, 101–103 (1981) [ JETP Lett. 33, 94–97 (1981)].

    Google Scholar 

  2. Aharonov, Y. & Bohm, D. Significance of electromagnetic potentials in the quantum theory. Phys. Rev. 115, 485–491 (1959).

    Article  ADS  MathSciNet  Google Scholar 

  3. Sharvin, D. Y. & Sharvin, Y. V. Magnetic-flux quantization in a cylindrical film of a normal metal. Pis'ma Zh. Eksp. Teor. Fiz. 34, 285–288 (1981) [ JETP Lett. 34, 272–275 (1982)].

    Google Scholar 

  4. Aronov, A. G. & Sharvin, Y. V. Magnetic-flux effects in disordered conductors. Rev. Mod. Phys. 59, 755–779 (1987).

    Article  ADS  Google Scholar 

  5. Gijs, M., Van Haesendonck, C. & Bruynseraede, Y. Resistance oscillations and electron localization in cylindrical Mg films. Phys. Rev. Lett. 52, 2069–2072 (1984).

    Article  ADS  CAS  Google Scholar 

  6. Pannetier, B., Chaussy, J., Rammal, R. & Gandit, P. Magnetic flux quantization in the weak-localization regime of a nonsuperconducting metal. Phys. Rev. Lett. 53, 718–721 (1984).

    Article  ADS  CAS  Google Scholar 

  7. Webb, R., Washburn, S., Umbach, C. & Laibowitz, D. C. Observation of h /e Aharonov–Bohm oscillations in normal-metal rings. Phys. Rev. Lett. 54, 2696–2699 (1985).

    Article  ADS  CAS  Google Scholar 

  8. Chandrasekhar, V., Rooks, M. J., Wind, S. & Prober, D. E. Observation of Aharonov–Bohm electron interference effect with period h /e and h /2e in individual micro-sized, normal-metal rings. Phys. Rev. Lett. 55, 1610–1613 (1985).

    Article  ADS  CAS  Google Scholar 

  9. Ijima, S. Helical microtubules of graphitic carbon. Nature 354, 56–58 (1991).

    Article  ADS  Google Scholar 

  10. Dresselhaus, M. S., Dresselhaus, G. & Eklund, P. C. Science of Fullerenes and Carbon Nanotubes (Academic, San Diego, 1986).

    Google Scholar 

  11. Langer, L. et al. Quantum transport in multiwalled carbon nanotubes. Phys. Rev. Let. 76, 479–482 (1996).

    Article  ADS  CAS  Google Scholar 

  12. Dai, H., Wong, E. W. & Lieber, C. M. Probing electrical transport in nanomaterials: conductivity of individual carbon nanotubes. Science 272, 523–526 (1996).

    Article  ADS  CAS  Google Scholar 

  13. Ebbesen, T. W. et al. Electrical conductivity of individual carbon nanotubes. Nature 382, 54–56 (1996).

    Article  ADS  CAS  Google Scholar 

  14. Tans, S. J. et al. Individual single-wall carbon nanotubes as quantum wires. Nature 386, 474–477 (1997).

    Article  ADS  CAS  Google Scholar 

  15. Bockrath, M. et al. Single-electron transport in ropes of carbon nanotubes. Science 275, 1922–1925 (1997).

    Article  CAS  Google Scholar 

  16. Bachtold, A. et al. Contacting carbon nanotubes selectively with low-ohmic contacts for four-probe electric measurements. Appl. Phys. Lett. 73, 274–276 (1998).

    Article  ADS  CAS  Google Scholar 

  17. Bachtold, A., Strunk, C., Schönenberger, C., Salvetat, J.-P. & Forró, L. in Proc. XIIth Int. Winterschool on Electronic Properties of Novel Materials (eds Kuzmany, H., Fink, J., Mehring, M. & Roth, S.) 65–68 (AIP, New York, 1998).

    Google Scholar 

  18. Frank, S., Poncharal, P., Wang, Z. L. & Heer, W. A. Carbon nanotube quantum resistors. Science 280, 1744–1746 (1998).

    Article  ADS  CAS  Google Scholar 

  19. Begmann, G. Weak localizations in thin films. Phys. Rep. 107, 1–56 (1984).

    Article  ADS  Google Scholar 

  20. Hamada, N., Sawada, D.-I. & Oshiyama, A. New one-dimensional conductors: graphite microtubules. Phys. Rev. Lett. 68, 1579–1581 (1992).

    Article  ADS  CAS  Google Scholar 

  21. Saito, R., Fujita, M., Dresselhaus, G. & Dresselhaus, M. S. Electronic structure of chiral graphene tubules. Appl. Phys. Lett. 60, 2204–2206 (1992).

    Article  ADS  CAS  Google Scholar 

  22. Mintmire, J. W., Dunlap, B. I. & White, C. T. Are fullerene tubules metallic? Phys. Rev. Lett. 68, 631–634 (1992).

    Article  ADS  CAS  Google Scholar 

  23. Wildöer, J. W. G., Venema, L. C., Rinzler, A. G., Smalley, R. E. & Dekker, C. Electronic structure of atomically resolved carbon nanotubes. Nature 391, 59–62 (1998).

    Article  ADS  Google Scholar 

  24. Odom, T. W., Huang, J.-L., Kim, P. & Lieber, C. M. Atomic structure and electronic properties of single-walled carbon nanotubes. Nature 391, 62–64 (1998).

    Article  ADS  CAS  Google Scholar 

  25. Wallace, P. R. The band theory of graphite. Phys. Rev. 71, 622–634 (1947).

    Article  ADS  CAS  Google Scholar 

  26. Miyamoto, Y. Mechanically stretched carbon nanotubes: Induction of chiral current. Phys. Rev. B 54, R11149–R11152 (1996).

    Article  ADS  CAS  Google Scholar 

  27. Ebbesen, T. W. & Ajayan, P. M. Large-scale synthesis of carbon nanotubes. Nature 358, 220–222 (1992).

    Article  ADS  CAS  Google Scholar 

  28. Bonard, J. M. et al. Purification and size-selection of carbon nanotubes. Adv. Mater. 9, 827–831 (1997).

    Article  CAS  Google Scholar 

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Acknowledgements

We thank H.-W. Fink, M. Henny, T. Hoss, M. Krüger, C. Terrier and V. Thommen for contributions. This work was supported by the Swiss National Science Foundation.

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Authors and Affiliations

  1. Institut für Physik, Universität Basel, Klingelbergstrasse, CH-4056 82, Basel, Switzerland

    Adrian Bachtold, Christoph Strunk, Thomas Nussbaumer & Christian Schönenberger

  2. Institut de Génie Atomique, École Polytechnique Fédérale de Lausanne, CH-1015, Lausanne, Switzerland

    Jean-Paul Salvetat, Jean-Marc Bonard & Laszló Forró

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  1. Adrian Bachtold
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Correspondence to Christian Schönenberger.

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Bachtold, A., Strunk, C., Salvetat, JP. et al. Aharonov–Bohm oscillations in carbon nanotubes. Nature 397, 673–675 (1999). https://doi.org/10.1038/17755

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