Electronic states of toroidal carbon nanotubes

Toroidal carbon nanotubes (TCN's) are threaded by magnetic flux (phi). The magneto-electronic structures are studied within the tight-binding model. The curvature effect, which is due to the misorientation of the pi-electron orbitals, might play an important role on the low energy electronic states. The thin TCN's, with armchair-zigzag and zigzag-armchair structures, exhibit four (three) types of energy gaps in the presence (absence) of the curvature effect. The magnetoelec tronic structures clearly vary with phi except the thin zigzag-armchair TCN's. They could exhibit the periodical Aharonov-Bohm oscillations, since the Zeeman splitting is generally negligible except at large phi's.