Theory of Exciton Energy Transfer in Carbon Nanotube Composites

We compute the exciton transfer (ET) rate between semiconducting single-wall carbon nanotubes (SWNTs). We show that the main reasons for the wide range of measured ET rates reported in the literature are 1) exciton confinement in local quantum wells stemming from disorder in the environment and 2) exciton thermalization between dark and bright states due to intratube scattering. The SWNT excitonic states are calculated by solving the Bethe-Salpeter equation using tight-binding basis functions. The ET rates due to intertube Coulomb interaction are computed via Fermi's golden rule. In pristine samples, the ET rate between parallel (bundled) SWNTs of similar chirality is very high ($\sim 10^{14}\;\text{s}^{-1}$) while the ET rate for dissimilar or nonparallel tubes is considerably lower ($\sim 10^{12}\;\text{s}^{-1}$). Exciton confinement reduces the ET rate between same-chirality parallel SWNTs by two orders of magnitude, but has little effect otherwise. Consequently, the ET rate in most measurements will be on the order of $ 10^{12}\;\text{s}^{-1}$, regardless of the tube relative orientation or chirality. Exciton thermalization between bright and dark states further reduces the ET rate to about $10^{11}\;\text{s}^{-1}$. The ET rate also increases with increasing temperature and decreases with increasing dielectric constant of the surrounding medium.