Confirmation of K-Momentum Dark Exciton Vibronic Sidebands Using 13C-Labeled, Highly Enriched (6,5) Single-Walled Carbon Nanotubes

A detailed knowledge of the manifold of both bright and dark excitons in single-walled carbon nanotubes (SWCNTs) is critical to understanding radiative and nonradiative recombination processes. Exciton-phonon coupling opens up additional absorption and emission channels, some of which may "brighten" the sidebands of optically forbidden (dark) excitonic transitions in optical spectra. In this report, we compare ¹²C and ¹³C-labeled SWCNTs that are highly enriched in the (6,5) species to identify both absorptive and emissive vibronic transitions. We find two vibronic sidebands near the bright ¹E ₁₁ singlet exciton, one absorptive sideband ∼200 meV above, and one emissive sideband ∼140 meV below, the bright singlet exciton. Both sidebands demonstrate a ∼50 cm ^-1 isotope-induced shift, which is commensurate with exciton-phonon coupling involving phonons of A ₁ ^' symmetry (D band, ω ∼ 1330 cm ^-1). Independent analysis of each sideband indicates that both sidebands arise from the same dark exciton level, which lies at an energy approximately 25 meV above the bright singlet exciton. Our observations support the recent prediction of, and mounting experimental evidence for, the dark K-momentum singlet exciton lying ∼25 meV (for the (6,5) SWCNT) above the bright γ-momentum singlet. This study represents the first use of ¹³C-labeled SWCNTs highly enriched in a single nanotube species to unequivocally confirm these sidebands as vibronic sidebands of the dark K-momentum singlet exciton.