Chirality-dependent environmental effects in photoluminescence of single-walled carbon nanotubes

The optical transition energies, $E_{11}$ and $E_{22}$, of single-walled carbon nanotubes (SWNTs) suspended in air have been investigated for 20 species by photoluminescence and excitation spectroscopies. We have studied the environmental effects in photoluminescence by comparing our results with those for the SWNTs wrapped by sodium-dodecyl-sulfate (SDS), as reported by Weisman and Bachilo [Nano Lett. 3, 1235 (2003)]. The energy differences between air-suspended and SDS-wrapped SWNTs, $\Delta E_{ii}=E_{ii}^{\text{air}}-E_{ii}^{\mathrm{SDS}}$, depends on the chiral vector $(n,m)$, specifically on the chiral angle and type of SWNT (type I or type II). The $\Delta E_{11}$ and $\Delta E_{22}$ mostly blueshifted, with the exception of the $\Delta E_{22}$ of some type II SWNTs (that have a small chiral angle), which redshifted. With an increase in the chiral angle, the $\Delta E_{11}$ increased in type I SWNTs and decreased in type II SWNTs. In contrast, the $\Delta E_{22}$ demonstrated opposite dependence on the chiral angle. The differences in $\Delta E_{11}$ and $\Delta E_{22}$ between type I and type II disappeared in the SWNTs with chiral angles close to 30° (near armchair). The $(n,m)$ dependence of the environmental effect on the transition energies can be explained by the difference in the effective mass, which contributes to the energy of Coulomb interactions between carriers.

Figure 1

Plan-view and bird-view (inset) SEM images of air-suspended SWNTs grown on a grated quartz substrate. Both the period and depth of a groove are $2\mu \mathrm{m}$. The SWNTs bridged in the groove during growth and aligned perpendicular to the groove.

Figure 2

(Color online) (a) PL map of air-suspended SWNTs, and (b) $E_{11}$ and $E_{22}$ of air-suspended SWNTs, compared to those of SDS-wrapped SWNTs reported by Weisman and Bachilo (see Ref. 2). Here, the closed squares and circles represent the air-suspended SWNTs, and the open squares and circles represent the SDS-wrapped SWNTs. The circles are type I $[(2n+m)\mathrm{mod}3=1]$ SWNTs, and squares are type II $[(2n+m)\mathrm{mod}3=2]$ SWNTs. Vectors indicate the energy shifts of $E_{11}$ and $E_{22}$ of the air-suspended SWNTs from those of SDS-wrapped SWNTs, $\Delta E_{11}$ and $\Delta E_{22}$. The broken line in (b) indicates a boundary between type I and type II.

Figure 3

$\Delta E_{11}$ and $\Delta E_{22}$ as a function of $1∕d_t$. The circles and squares represent type I and type II, respectively. The solid lines connect SWNTs belonging to the same $2n+m=\text{constant}$ family.

Figure 4

$\Delta E_{11}$ and $\Delta E_{22}$ as a function of $\theta$. The circles and squares represent type I and type II, respectively. The $\Delta E_{11}$ and $\Delta E_{22}$ show the obvious $\theta$ dependencies. $\Delta E_{11}$ decreases in type I SWNTs and increases in type II SWNTs with an increase in $\theta$. $\Delta E_{22}$ shows the opposite dependencies. The difference between type I and type II SWNTs disappears for the near-armchair SWNTs $(\theta \sim 30°)$.

Figure 5

$\Delta E_{11}-m_1$ and $\Delta E_{22}-m_2$ plots. The circles and squares represent type I and type II, respectively. The $\Delta E_{11}$ and $\Delta E_{22}$ are smaller for the larger effective mass.