Electronic structures of chiral carbon toroids

The π-electronic states of chiral carbon toroids are calculated from the tight-binding model. The electronic structures, the energy gap, the energy spacing and the degeneracy of discrete states, are studied. They are mainly determined by the geometric structures (height, chiral angle and radius) the curvature effect and the magnetic flux (φ). Carbon toroids have four (three) types of energy gaps, while the curvature effect is important (negligible). The relations between energy gaps and geometric structures are complex (simple) in the presence (absence) of the curvature effect. The φ-dependent electronic structures exhibit the periodic Aharonov-Bohm oscillations. The magnetic flux could also effectively affect the state degeneracy of zigzag carbon toroids.