Quantification of curvature effects in boron and carbon nanotubes: Band structures and ballistic current

The zone-foldingmethod is a widely used technique in computing the electronic structure of carbon nanotubes. In this paper, curvature effects of boron and carbon nanotubes of different diameters and chiralities are systematically quantified using the density-functional-based tight-binding method. Here, the curvature effect in a nanotube is defined as the difference between the one-dimensional band structure calculated from the tubular atomic structure and the band structure calculated from the related two-dimensional sheet with the zone-folding method. For each nanotube, we quantify this difference by calculating the standard deviation of the band energies sigma(E) and the maximal relative deviation between the derived ballistic currents delta I-max. For all considered nanotubes with diameters d > 2 nm, the standard deviation sigma(E) is below 60 meV and decreases only slowly, whereas delta I-max is still as large as 8% and does not tend to zero for large d.