Aharonov–Bohm oscillations in carbon nanotubes

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.