Abstract
We have calculated the bright-dark energy splitting in semiconducting zigzag carbon nanotubes in a simple tight-binding model for π -electrons . The short-range cut-off of the Coulomb interaction is used as a fitting parameter. We have found that the splitting depends not only on the type of transition, E 11 or E 22 , but also on the structure, or the index, of carbon nanotube, and that family pattern appears in the cut-off parameter dependence of the splitting.
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