Magneto-optical spectroscopy of highly aligned carbon nanotubes: Identifying the role of threading magnetic flux

We have investigated excitons in highly aligned single-walled carbon nanotubes (SWCNTs) through optical spectroscopy at low temperatures down to 1.5 K and high magnetic fields (B) up to 55 T. SWCNT/polyacrylic acid films were stretched, giving SWCNTs that are highly aligned along the direction of stretch ( ̂ \^n). Utilizing two well-defined measurement geometries, ̂ \^n∥B and ̂ \^n⊥B, we provide unambiguous evidence that the photoluminescence energy and intensity are only sensitive to the B-component parallel to the tube axis. A theoretical model of one-dimensional magnetoexcitons, based on exchange-split ``bright'' and ``dark'' exciton bands with Aharonov-Bohm-phase-dependent energies, masses, and oscillator strengths, successfully reproduces our observations and allows determination of the splitting between the two bands as ~4.8 meV for (6,5) SWCNTs.