Defects Enable Dark Exciton Photoluminescence in Single-Walled Carbon Nanotubes

Variable temperature photoluminescence excitation spectroscopy of three (n,m) species of single-walled carbon nanotubes revealed that at resonant S₂₂ excitation, in addition to allowed excitonic optical transitions, several sidebands that should be forbidden based on selection rules were observed and appeared to have a strong temperature dependence. In particular, we found that a sideband located approximately 130 meV away from the bright S₁₁ exciton peak relating to the K-momentum dark exciton state, called X₁, decreased in intensity five-fold as the samples were cooled. Direct optical excitation of this dark state is nominally forbidden, thus calling into question how the state is populated, and why it is so prominent in the photoluminescence spectrum. Interestingly, the ratio of the integrated photoluminescence intensities of X₁ to S₁₁ scales with a Boltzmann factor unrelated to the phonon that is thought to be responsible for depopulating the K-momentum dark exciton state: an in-plane transverse optical phonon, A₁'. Furthermore, photoluminescence spectra from individual (7,5) nanotubes show that only a small fraction exhibit the X₁ feature, with varying oscillator strength, thus suggesting that intrinsic processes such as phonon scattering are not responsible for populating the dark state. Alternatively, we suggest that populating the K-momentum dark exciton state requires scattering from defects, which is consistent with the increased magnitude of the X₁ feature for samples with increased sample purification and processing. Thus, the presence of an X₁ peak in photoluminescence is an extremely sensitive spectroscopic indicator of defects on single-walled carbon nanotubes.