We report high field magneto-optical study on the first and second sub-bandtransitions of single-chirality single-walled carbon nanotubes. The orderingand relative energy splitting between bright and dark excitonic states werefound to be inverse between the first and second subbands. We verified that thezero-momentum dark singlet exciton lies below the bright exciton for the firstsubband transitions, while for the second sub-band transitions, it was found tohave higher energy than the bright excitonic state. Effect of this peculiarexcitonic structure was found to manifest itself in distinctive Aharonov-Bohmsplitting in ultra-high magnetic fields up to 190 T.
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