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

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

2009-08-10

arxiv.org/abs/0908.1399v2

Phys. Rev. B 81 155123 (2010)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

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

Scientific paper

10.1103/PhysRevB.81.155123

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 $K_{A_1'}$ 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.

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