Effects of valley mixing and exchange on excitons in carbon nanotubes with Aharonov-Bohm flux

摘要

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.