Density of states reflects diameter in nanotubes

Dresselhaus1 asked recently why scanning tunnelling microscopy and spectroscopy experiments2,3 find a similar number of peaks, in the density of states near the Fermi level, for a range of semiconducting single-wall carbon nanotubes with roughly the same diameters. After all, semiconducting achiral zigzag single-wall nanotubes can have translational unit cells more than an order of magnitude smaller than those of chiral semiconducting single-wall nanotubes with a similar diameter, so they might be expected to have fewer but sharper peaks in their density of states1. We show that all semiconducting single-wall nanotubes with similar diameters should have a similar density of states near the Fermi level, independent of translational unit cell size or chiral angle.