Band structure calculations show that carbon nanotubes exist as either
metals or semiconductors, depending on diameter and degree of helicit
y. When the diameters of the nanotubes become comparable to the electr
on wavelength, the band structure becomes noticeably one-dimensional.
Scanning tunneling microscopy and spectroscopy data on nanotubes with
outer diameters from 2 to 10 nm show evidence of one-dimensional behav
ior: the current-voltage characteristics are consistent with the funct
ional energy dependence of the density-of-states in 1D systems. The me
asured energy gap values vary linearly with the inverse nanotube diame
ter. Electrical resistivity acid magnetoresistance measurements have b
een reported for larger bundles, and the temperature dependence of the
electrical resistance of a single micro-bundle was found to be simila
r to that of graphite and its magnetoresistance was consistent with th
e formation of Landau levels. Magnetic susceptibility data taken on bu
ndles of similar tubes reveal a mostly diamagnetic behavior. The susce
ptibility al fields above the value at which the magnetic length equal
s the tube diameter has a graphite-like dependence on temperature and
field. At low fields, where electrons sample the effect of the finite
tube diameter, the susceptibility has a much more pronounced temperatu
re dependence.