Localized and Delocalized Electronic States in Single-Wall Carbon Nanotubes

We present momentum-dependent measurements of the density response function of bulk samples of purified single-wall nanotubes probed by electron energy loss spectroscopy. Carbon nanotubes support excitations between both delocalized and localized electronic states. The $\pi$ plasmon exhibits a q dependence similar to that of the graphite plane, signaling the graphitelike nature of the nanotube electron system along the tube axis. In contrast, the interband excitations between the singularities in the nanotube electronic density of states observed at low energy have vanishingly small dispersion in q, and can be used to show that our samples contain significant quantities of semiconducting and metallic single-wall nanotubes.