Persistent currents in toroidal carbon nanotubes

The geometric structure of the toroidal carbon nanotubes (TCN’s) determines the electronic structure and thus the characteristics of the persistent current. Such current is caused by the magnetic flux φ through TCN’s. The semiconducting TCN’s exhibit diamagnetism at small φ, which is in great contrast with paramagnetism of the metallic TCN’s. The induced magnetic moment is proportional to the toroid radius, but independent of the toroid width. The magnetic response is weak, while it is much stronger than that of a mesoscopic semiconductor or metal ring. The persistent current is a linearly periodical function of φ, with a period ${\phi }_0\mathrm{}(hc/e).$ Such an oscillation is the manifestation of the Aharonov-Bohm (AB) effect. Temperature $\mathrm{}\left(T\right)\mathrm{}$ does not destroy the periodical AB oscillation, although it would significantly reduce the persistent currents. The Zeeman splitting may lead to the destruction of the periodicity at very large φ. A larger TCN at lower $T$ and φ is relatively suitable for verifying the AB effect.