π-electron theory of transverse optical excitons in semiconducting single-walled carbon nanotubes

Abstract

We present a quantitative theory of optical absorption polarized transverse to the tube axes in semiconducting single-walled carbon nanotubes. Within one-electron theory, transverse optical absorption occurs at an energy that is exactly in the middle of the two lowest longitudinal absorption energies. For nonzero Coulomb interactions between the $\ensuremath{\pi}$ electrons, transverse optical absorption is to an exciton state that is strongly blueshifted relative to the longitudinal excitons. Very similar behavior is observed in the $\ensuremath{\pi}$-conjugated polymer polyparaphenylenevinylene, where the optical absorption polarized predominantly perpendicular to the polymer chain axis is blueshifted relative to the absorptions polarized predominantly along the chain axis. The binding energy of the transverse exciton in the nanotubes is considerably smaller than those of the longitudinal excitons. Electron-electron interactions also reduce the relative oscillator strength of the transverse optical absorption. Our theoretical results are in excellent agreement with recent experimental measurements in four chiral nanotubes.