Low-energy electronic properties of pairs of identical carbon nanotubes

The tight-binding model is employed to study the low-energy electronic properties of aligned pairs of identical single-wall carbon nanotubes with the intertube interactions. The rotational symmetry about the tube axes is totally broken, and the intertube interactions hybridize the atomic states on each tube to create new sub-bands. Sub-band spacing, sub-band curvature, band-edge states, and energy gaps are sensitive to stacking types and are also dependent on the radius and the chirality of the tubes. The systems could be metal, semimetal, or semiconductor depending on their stacking types. In particular, an armchair pair keeps the band structures linear like a single tube if the pair has a glide symmetry with respect to the plane between its constituent tubes. Breaking this symmetry makes the pair semimetallic or semiconducting. However, there are no such properties for chiral and zigzag pairs. The variations in electronic structures of these pairs are more complicated and more sensitive to the tube radii. Instead of being like a rope or a large bundle, the stacking-type dependent behavior is more similar to commensurate double-wall carbon nanotubes.