Transmission Through Carbon Nanotubes with Polyhedral Caps

We study electron transport between capped carbon nanotubes and a substrate, and relate this transport to the local density of states in the cap. Our results show that that the transmission probability mimics the behavior of the density of states at all energies except those that correspond to localized states. For a capped carbon nanotube that is not connected to a substrate, the localized states do not couple to the coexisting continuum states. However, close proximity of a substrate causes hybridization between these states. As a result, new transmission paths open from substrate states to nanotube continuum states via the localized states in the cap. We show that the interference between various paths gives rise to transmission antiresonances with the minimum equal to zero at the energy of the localized state. The presence of defects in the tube places close to the cap transforms antiresonances into resonances. Depending on the spatial position of defects, these resonant states are capable of carrying a large current. The results of this paper are of relevance to carbon nanotube based studies on molecular electronics and probe tip applications.