ELECTRONIC STATES OF CARBON NANOTUBES

The pi-electron states of carbon nanotubes (CN's) in magnetic fields are calculated in the effective-mass theory. A sensitive change of CN from metal to semiconductor depending on its structure is well reproduced. The band gap is inversely proportional to the tube diameter and exhibits a drastic change as a function of magnetic flux passing through the cylinder with period ch/e due to the Aharonov-Bohm effect. In a magnetic field perpendicular to the tube axis, the band-gap is reduced strongly and the energy spectra approach those of a graphite sheet.