  It has been shown that the two different orientations of Stone-Wales (SW)
defects, i.e. longitudinal and circumferential SW defects, on carbon nanotubes
(CNTs) result in two different electronic structures. Based on density
functional theory we have shown that the longitudinal SW defects do not open a
bandgap near the Fermi energy, while a relatively small bandgap emerges in
tubes with circumferential defects. We argue that the bandgap opening in the
presence of circumferential SW defects is a consequence of long-range symmetry
breaking which can spread all the way along the tube. Specifically, the
distribution of contracted and stretched bond lengths due to the presence of
defects, and hopping energies for low-energy electrons, i.e. the 2pz electrons,
show two different patterns for the two types of defects. Interplay between the
geometric features and the electronic properties of the tubes have also been
studied for different defect concentrations. Considering $\pi$-orbital charge
density, it has also been shown that the deviations of bond lengths from their
relaxed length result in different doping for two defect orientations around
the defects -- electron-rich for a circumferential defect and hole-rich for a
longitudinal one. We have also shown that, in the tubes having both types of
defects, circumferential defects would dominate and impose their electronic
properties.
