Many-electron effects often dramatically modify the properties of reduced
dimensional systems. We report calculations, based on an many-electron Green's
function approach, of electron-hole interaction effects on the optical spectra
of small-diameter single-walled carbon nanotubes. Excitonic effects
qualitatively alter the optical spectra of both semiconducting and metallic
tubes. Excitons are bound by ~ 1 eV in the semiconducting (8,0) tube and by ~
100 meV in the metallic (3,3) tube. These large many-electron effects explain
the discrepancies between previous theories and experiments.Comment: 6 pages, 3 figures, 2 table