Optical Signatures of the Aharonov-Bohm Phase in Single-Walled Carbon Nanotubes

We report interband magneto-optical spectra for single-walled carbon nanotubes in high magnetic fields up to 45 tesla, confirming theoretical predictions that the band structure of a single-walled carbon nanotube is dependent on the magnetic flux ϕ threading the tube. We have observed field-induced optical anisotropy as well as red shifts and splittings of absorption and photoluminescence peaks. The amounts of shifts and splittings depend on the value of ϕ/ϕ and are quantitatively consistent with theories based on the Aharonov-Bohm effect. These results represent evidence of the influence of the Aharonov-Bohm phase on the band gap of a solid.