Energies of π*- and π-states of the conduction band and valence band of chiral carbon nanotubes

Abstract

Nanotubes (NTs) are mainly represented by (n,p) chiral NTs with chirality indices 0 < p < n delimited by (n,0) and (n,n) for achiral NTs. In (n,p) chiral NTs, the unit cell hexagons have a helical arrangement on the cylindrical surface of an NT and common angular and axial translations. An analytical formula was derived for calculation of the band structure of both chiral and achiral NTs with chirality indices 0 ≤ p ≤ n and band diagrams of some chiral NTs. Chiral NTs significantly extend the range of semiconducting NTs. An equation for the band gap width ΔЕ of semiconducting chiral and achiral NTs was derived: \(\frac{{\vartriangle E}}{{{\gamma _0}}} = \frac{{2\pi }}{{\sqrt {3{n^2} + 3np + 3{p^2}} }}\). Tables of the band structure parameters of metallic and semiconducting chiral NTs are presented.