Magnetic brightening of ``dark'' excitons in carbon nanotubes

We have measured polarized-excitation photoluminescence (PL) on micelle-suspended single-walled carbon nanotubes (SWNTs) in aqueous solution in external magnetic fields ($B)$ up to 45 T at room temperature. Each PL peak, corresponding to a specific chirality, splits into two in a $B$ and the amount of splitting increases with $B$. The magnetic field dependence of the relative intensities of the two peaks reveals that the lower-energy peak increases in intensity (or ``brightens'') with increasing $B$. These results can be understood in terms of ``magnetic brightening'' of an excitonic state that is ``dark'' at 0 T. Namely, recent calculations taking into account intervalley Coulomb mixing in semiconducting SWNTs predict the existence of a dark excitonic state at an energy $\Delta _{X}$ below the lowest optically active (bright) excitonic state. On the other hand, magnetic flux \textit{$\phi $} threading a nanotube removes the intervalley degeneracy which is seen in absorption measurements as peak splittings by an amount $\Delta _{AB}$ proportional to \textit{ $\phi $} (when \textit{$\phi $/$\phi $}$_{0} \quad \le $ 1/6, \textit{$\phi $}$_{0}$: magnetic flux quantum). While two equally-bright excitonic peaks are predicted and observed at high fields ($\Delta _{AB} \quad >> \quad \Delta _{X})$,$^{1}$ magnetic brightening is expected at lower fields ($\Delta _{AB} \quad \sim \quad \Delta _{X})$, which is consistent with our observations. $^{1}$ S. Zaric \textit{et al}, Phys. Rev. Lett., to appear (see also cond-mat/0509429)