($n$,$m)$-dependent environmental effect on photoluminescence of single-walled carbon nanotubes

The photoluminescence (PL) map was measured for 20 chiralities of single-walled carbon nanotubes (SWNTs) suspended in air, and the $E_{11}$ and $E_{22}$ were compared to the results reported for SDS-wrapped SWNTs [1]. The $E_{11}$ and $E_{22}$ are mostly blueshifted by a few tens of meV, except for $E_{22}$ of type-II near zigzag SWNTs which show a redshift. The energy shifts of $E_{11}$ and $E_{22}$ from those of SDS-wrapped SWNTs, $\Delta E_{11}$ and $\Delta E_{22}$, show clear dependence on the chirality, in particular on the chiral angle rather than the diameter. $E_{11}$ and $E_{22}$ show different dependences on the chiral angle between type-I and type-II SWNTs. In the case of type-I SWNTs, $\Delta E_{11}$ is lager for the larger chiral angle whereas $\Delta E_{22}$ is smaller for the larger chiral angle. In contrast, type-II SWNTs shows the opposite dependences. The difference between type-I and type-II disappears for the SWNTs with the chirality near armchair. The chiral angle dependence of environmental effect can be explained by difference in effective mass. [1] R. B. Weisman \textit{et al}. \textit{Nano Lett. }\textbf{3 }1235(2003).