Controlling edge states of zigzag carbon nanotubes by the Aharonov-Bohm flux

It has been known theoretically that localized states exist around zigzag edges of a graphite ribbon and of a carbon nanotube, whose energy eigenvalues are located between conduction and valence bands. We found that in metallic single-walled zigzag carbon nanotubes two of the localized states become critical, and that their localization length is sensitive to the mean curvature of a tube and can be controlled by the Aharonov-Bohm flux. The curvature induced mini-gap closes by the relatively weak magnetic field. Conductance measurement in the presence of the Aharonov-Bohm flux can give information about the curvature effect and the critical states.