Band-edge Exciton States in a Single-walled Carbon Nanotube Revealed by Ultra-high Magnetic Field Magneto-optical Spectroscopy

We report high field magneto-optical study on the first and second sub-band transitions of highly-purified (6,5) single-walled carbon nanotubes. The ordering and relative energy splitting between bright and dark excitonic states were found to be highly sub-band index dependent. We verified that the zero-momentum dark singlet exciton lies below the bright exciton for the first sub-band transitions, while for the second sub-band transitions, it was found to have higher energy than the bright excitonic state. Effect of this peculiar excitonic structure was found to manifest itself in distinctive Aharonov-Bohm splitting in ultra-high magnetic fields up to 190 T.