Only optically active excitons can be identified by transient absorption spectroscopy, and the actual mechanisms of exciton relaxation in nanoscale systems remain unknown as dipole-forbidden transitions and charge-transfer states are not accounted for. Focusing on interacting (6,4) and (8,4) carbon nanotubes (CNTs), we show that dark excitons largely determine the relaxation pathways for photogenerated excitons in CNT bundles. New channels appear involving asymmetric electron-hole excitations within the same CNT and charge-transfer states, in which the electron and hole are confined to separate CNTs. The energy and charge transfers are facilitated by coupling to both low- and high-frequency phonons. Radial breathing modes are particularly important because they distort the CNT geometry, induce crossings of electronic states, and modulate coupling between CNTs. The time domain simulations reported herein uncover the quantum states and phonon modes that contribute to exciton relaxation in a CNT cluster, elucidating the complete relaxation mechanism. The established role of optically dark states pertains to nonequilibrium dynamics in nanoscale materials in general.
Keywords: carbon nanotubes; charge and energy transfer; electron vibrational relaxation; excitons; nonadiabatic molecular dynamics; time domain density functional theory.