Electronic and Optical Properties of Narrow-Gap Carbon Nanotubes

Abstract

The s p 3 tight-binding model is used to calculate electronic structures of narrow-gap carbon nanotubes. The curvature effects cause a small energy gap, a one-dimensional parabolic bands, and a shift in the Fermi wave vector. The energy gap is described by the approximate relation E g ≃5| V p p π | b 2 cos (3θ)/16 R d 2 . It is almost identical to the first-principles result. Due to the curvature effects, the optical spectra exhibit single-particle absorption peaks and a plasmon structure. They are consistent with the experimental results, the absorption peaks in the optical conductivity and the plasmon edge in the reflectance spectrum, thereby verifing the relation between E g and ( R d ,θ).