Quasiparticle energies, excitonic effects and optical absorption spectra of small-diameter single-walled carbon nanotubes

We present a first-principles study of the effects of many-electron interactions on the optical properties of single-walled carbon nanotubes. Motivated by recent experiments, we have carried out ab initio calculations on the single-walled carbon nanotubes (3, 3), (5, 0) and (8, 0). The calculations are based on a many-body Green's function approach in which both the quasiparticle (single-particle) excitation spectrum and the optical (electron-hole excitation) spectrum are determined. We show that the optical spectrum of both the semiconducting and metallic nanotubes studied exhibits important excitonic effects due to their quasi-one-dimensional nature. Binding energies for excitonic states range from zero for the metallic (5, 0) tube to nearly 1 eV for the semiconducting (8, 0) tube. Moreover, the metallic (3, 3) tube possesses exciton states bound by nearly 100 meV. Our calculated spectra explain quantitatively the observed features found in the measured spectra.