Effects of Valley Mixing and Exchange on Excitons in Carbon Nanotubes with Aharonov–Bohm Flux

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Because of the presence of two valleys and the electron spin, the exciton states have a degeneracy of 16 in the lowest order k·p approximation. Due to a weak short-range part of the Coulomb interaction, they are split into several levels, leaving only a single optically-active bright level and making all others optically-inactive or dark. Their ordering and energy splitting are shown to be determined by two parameters characterizing the short-range interaction, sensitive to detailed form of the potential and wave function. The presence of a magnetic flux through the cross section, accessible experimentally, modifies these energy levels strongly and causes the appearance of two bright excitons.

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