Decay Dynamics and Diffusion Lengths of Bright and Dark Excitons in Air-Suspended Carbon Nanotubes

Abstract

As excitonic states play an important role in optical phenomena [1] in carbon nanotubes, their fundamental properties such as emission lifetime and diffusion length have been studied by various optical techniques [2]. In the lowest lying states of excitons, however, there exist other “dark” states, whose properties are not well understood yet because they are not optically accessible. Here we separately investigate exciton dynamics of parity-odd bright state and parity-even dark state by performing time-resolved photoluminescence measurements on defect-free as-grown carbon nanotubes. The emission decay curves exhibit bi-exponential behavior, where the fast and slow decay components arise from the dynamics of bright and dark excitons, respectively. We analyze such exciton dynamics using a three-level model including the effects of end quenching by measuring chirality-identified nanotubes with different suspended lengths [Fig. 1]. We find that bright excitons have lifetimes of ~70 ps and diffusion lengths of several hundred nanometers, consistent with the known values. In comparison, dark excitons have much longer lifetimes in the order of nanoseconds and diffusion lengths longer than 3 μm. We also observe a tendency that nanotubes with larger diameter have higher bright-dark transition rate, which is likely due to the diameter dependence of the splitting energy between bright and dark states. Work supported by JSPS (KAKENHI JP16K13613 and JP17H07359), MEXT (Nanotechnology Platform), and RIKEN (Incentive Research Project). H.M. acknowledges support by RIKEN Junior Research Associate Program. [1] A. Ishii, T. Uda, Y. K. Kato, Phys. Rev. Appl. 8, 054039 (2017).[2] A. Ishii, M. Yoshida, Y. K. Kato, Phys. Rev. B 91, 125427 (2015).Fig.1 Emission decay curves obtained from (9,8) nanotubes with various lengths ranging from 0.5 μm (purple) to 4.2 μm (red). The gray line indicates the instrument response function. (inset) Schematic of the three-level model for exciton decay dynamics. Figure 1