Electron–electron interaction effects on the photophysics of metallic single-walled carbonnanotubes

Abstract

Single-walled carbon nanotubes are strongly correlated systems withlarge Coulomb repulsion between two electrons occupying the samepz orbital. Within a molecular Hamiltonian appropriate for correlatedπ-electron systems, we show that optical excitations polarized parallel to thenanotube axes in the so-called metallic single-walled carbon nanotubes areexcitons. Our calculated absolute exciton energies in twelve different metallicsingle-walled carbon nanotubes, with diameters in the range 0.8–1.4 nm, are innearly quantitative agreement with experimental results. We have also calculatedthe absorption spectrum for the (21, 21) single-walled carbon nanotube in theE22 region. Our calculated spectrum gives an excellent fit to the experimental absorptionspectrum. In all cases our calculated exciton binding energies are only slightly smaller thanthose of semiconducting nanotubes with comparable diameters, in contradiction to resultsobtained within the ab initio approach, which predicts much smaller binding energies. Weascribe this difference to the difficulty of determining the behavior of systems withstrong on-site Coulomb interactions within theories based on the density functionalapproach. As in the semiconducting nanotubes we predict in the metallic nanotubes atwo-photon exciton above the lowest longitudinally polarized exciton that canbe detected by ultrafast pump-probe spectroscopy. We also predict a subgapabsorption polarized perpendicular to the nanotube axes below the lowest longitudinalexciton, blueshifted from the exact midgap by electron–electron interactions.