Chirality Dependence of the $K$-Momentum Dark Excitons in Carbon Nanotubes

Abstract

Using a collection of twelve semiconducting carbon nanotube samples, each highly enriched in a single chirality, we study the chirality dependence of the $K$-momentum dark singlet exciton using phonon sideband optical spectroscopy. Measurements of bright absorptive and emissive sidebands of this finite momentum exciton identify its energy as 20 - 38 meV above the bright singlet exciton, a separation that exhibits systematic dependencies on tube diameter, $2n+m$ family, and semiconducting type. We present calculations that explain how chiral angle dependence in this energy separation relates to the Coulomb exchange interaction, and elaborate the dominance of the $K_{A_1^{\prime }}$ phonon sidebands over the zone-center phonon sidebands over a wide range of chiralities. The Kataura plot arising from these data is qualitatively well described by theory, but the energy separation between the sidebands shows a larger chiral dependence than predicted. This latter observation may indicate a larger dispersion for the associated phonon near the $K$ point than expected from finite distance force modeling.

24 pages, 12 figures, 1 table; slight title change, Figures 1 and 11 added, reference added, presentation improved throughout document

References in corpus (9)

• Exciton binding energies in carbon nanotubes from two-photon photoluminescence
• Optical Phonons in Carbon Nanotubes: Kohn Anomalies, Peierls Distortions and Dynamic Effects
• The phonon dispersion of graphite by inelastic x-ray scattering
• Electron-electron interaction effects on optical excitations in semiconducting single-walled carbon nanotubes
• Diameter and Chirality Dependence of Exciton Properties in Carbon Nanotubes
• Absorption spectroscopy of individual single-walled carbon nanotubes
• Magnetic Brightening of Carbon Nanotube Photoluminescence through Symmetry Breaking
• Defect Induced Photoluminescence from Dark Excitonic States in Individual Single-Walled Carbon Nanotubes
• Photoluminescence sidebands of carbon nanotubes below the bright singlet excitonic levels: Coupling between dark excitons and K-point phonons

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• Survey of Exciton-Phonon Sidebands by Magneto-optical Spectroscopy Using Highly Purified (6,5) Single-walled Carbon Nanotubes
• Exciton-phonon Bound Complex in Single-walled Carbon Nanotubes Revealed by High-field Magneto-optical Spectroscopy
• Intrinsic process for upconversion photoluminescence via $K$-momentum phonon coupling in carbon nanotubes