Magnetic Brightening of Dark Excitons in Individual Single-Walled Carbon Nanotubes*

We have performed micro-photoluminescence (PL) studies on \textit{individual} single-walled carbon nanotubes (SWNTs) at varying temperatures ($T$ = 4 K -- 100 K) in magnetic fields ($B)$ up to 5 T, which provide direct evidence for the existence of dark excitons in SWNTs. Only when the $B$ was parallel to the tube axis, we observed the appearance of a \textit{secondary peak at a lower energy} with respect to the main emission peak. The secondary peak increased in intensity with increasing $B$ at the expense of the main peak. At the lowest $T$, a complete reversal of emission intensity from the main peak to the side peak was seen as the $B$ was increased. However, the main peak was recovered as the $T$ was increased at a fixed $B$. These behaviors can be explained by assigning the main and secondary peaks to the lowest-energy bright and dark singlet exciton states, respectively. The absence of these behaviors in $B$ perpendicular to the tube axis convincingly suggests that brightening is induced by the Aharonov-Bohm phase. The zero-field dark-bright splitting is found to be $\sim $1-2 meV, which is lower than most theoretical predictions.