The remarkable transport properties of carbon nanotubes (CNTs) are determined by their unusual electronic structure. The electronic states of a carbon nanotube form one-dimensional electron and hole sub-bands, which, in general, are separated by an energy gap. States near the energy gap are predicted to have an orbital magnetic moment, μ_(orb), that is much larger than the Bohr magneton (the magnetic moment of an electron due to its spin). This large moment is due to the motion of electrons around the circumference of the nanotube, and is thought to play a role in the magnetic susceptibility of CNTs and the magneto-resistance observed in large multiwalled CNTs. But the coupling between magnetic field and the electronic states of individual nanotubes remains to be quantified experimentally. Here we report electrical measurements of relatively small diameter (2-5 nm) individual CNTs in the presence of an axial magnetic field. We observe field-induced energy shifts of electronic states and the associated changes in sub-band structure, which enable us to confirm quantitatively the predicted values for μ_(orb).
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