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Diameter and Chirality Dependence of Exciton Properties in Carbon Nanotubes

Rodrigo B. Capaz·Catalin D. Spataru·Sohrab Ismail-Beigi·Steven G. Louie
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Abstract

We calculate the diameter and chirality dependences of the binding energies, sizes, and bright-dark splittings of excitons in semiconducting single-wall carbon nanotubes (SWNTs). Using results and insights from {\it ab initio} calculations, we employ a symmetry-based, variational method based on the effective-mass and envelope-function approximations using tight-binding wavefunctions. Binding energies and spatial extents show a leading dependence with diameter as $1/d$ and $d$, respectively, with chirality corrections providing a spread of roughly 20% with a strong family behavior. Bright-dark exciton splittings show a $1/d^2$ leading dependence. We provide analytical expressions for the binding energies, sizes, and splittings that should be useful to guide future experiments.

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Rodrigo B. Capaz, Catalin D. Spataru, Sohrab Ismail-Beigi, Steven G. Louie. 2006-06-18. Diameter and Chirality Dependence of Exciton Properties in Carbon Nanotubes. https://doi.org/10.1103/physrevb.74.121401

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