First-passage theory of exciton population loss in single-walled carbon nanotubes reveals micron-scale intrinsic diffusion lengths

Abstract

One-dimensional crystals have long range translational invariance which manifests as long exciton diffusion lengths, but such intrinsic properties are often obscured by environmental perturbations. We use a first-passage approach to model single-walled carbon nanotube (SWCNT) exciton dynamics (including exciton-exciton annihilation and end effects) and compare it to results from both continuous-wave and multipulse ultrafast excitation experiments to extract intrinsic SWCNT properties. Excitons in suspended SWCNTs experience macroscopic diffusion lengths, on the order of the SWCNT length (1.3--4.7 $\ensuremath{\mu}$m), in sharp contrast to encapsulated samples. For these pristine samples, our model reveals intrinsic lifetimes (350--750 ps), diffusion constants (130--350 cm${}^{2}$/s), and absorption cross sections (2.1--$3.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ cm${}^{2}$/atom) among the highest previously reported.