Electronic and optical properties of narrow-gap carbon nanotubes

The sp(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 hands, and a shift in the Fermi wave vector. The energy gap is described by the approximate relation E-g similar or equal to 5\V-pppi\b(2) cos(3theta)/16R(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, theta).