Diameter and Chirality Dependence of Exciton Properties in Carbon Nanotubes

Details Diameter and Chirality Dependence of Exciton Properties in Carbon Nanotubes Diameter and Chirality Dependence of Exciton Properties in Carbon Nanotubes

2006-06-18

arxiv.org/abs/cond-mat/0606474v1

Physics

Condensed Matter

Materials Science

Scientific paper

10.1103/PhysRevB.74.121401

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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