Aharonov–Bohm oscillations in carbon nanotubes

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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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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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Correspondence to Christian Schönenberger.

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