Magneto-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 temperature (1.5 K) and high magnetic fields ($\textbf{\textit{B}}$) up to 55 T. SWCNT/polyacrylic acid films were stretched, giving SWCNTs that are highly aligned along the direction of stretch ($\hat{n}$). Utilizing two well-defined measurement geometries, $\hat{n}\parallel\textbf{\textit{B}}$ and $\hat{n}\perp\textbf{\textit{B}}$, we provide unambiguous evidence that the photoluminescence energy and intensity are only sensitive to the $\textbf{\textit{B}}$-component parallel to the tube axis. A theoretical model of one-dimensional magneto-excitons, 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 $\sim4.8$ meV for (6,5) SWCNTs.