Exciton Resonances Quench the Photoluminescence of Zigzag Carbon Nanotubes

We show that the photoluminescence intensity of single-walled carbon nanotubes is much stronger in tubes with large chiral angles—armchair tubes—because exciton resonances make the luminescence of zigzag tubes intrinsically weak. This exciton-exciton resonance depends on the electronic structure of the tubes and is found more often in nanotubes of the $+1$ family. Armchair tubes do not necessarily grow preferentially with present growth techniques; they just have stronger luminescence. Our analysis allows us to normalize photoluminescence intensities and find the abundance of nanotube chiralities in macroscopic samples.

Figure 1

(a) PL process: $e{h}_{22}$ excitation from the ground state (GS) by photon absorption (solid arrow), relaxation to $e{h}_{11}$ (dashed arrow), and emission (solid arrow) of $h{\nu }_{11}$. The relaxation step separates nanotubes into (b) those with only one decay channel and (c) those where $e{h}_{22}$ can decay into two $e{h}_{11}$; (d) excitonic density of states (schematic).

Figure 2

(a) Bars: measured wavelength and intensity of the maximum photoluminescence excitation (PLE) signal for the $(11,1)$ and $(10,2)$ in solution. The emission is at 0.98 and 1.18 eV for the $(11,1)$ and $(10,2)$, respectively [2, 4]. Lines: calculated absorption (see text). (b) Tube families: $p=0$ (green, italic), $-1$ (red, bold), and $+1$ (blue, roman).

Figure 3

(a) Solid symbols: experimental bare exciton energies; open symbols: calculated. Solid lines connect tubes in a branch ($2n+m=\mathrm{const}$); dashed lines tubes with largest chiral angles (close to armchair); squares are zigzag tubes. (b) Ratio of $E_{22}$ and $E_{11}$ for three branches. The dashed blue line is the as measured ratio $h{\nu }_{22}/h{\nu }_{11}$ [2].

Figure 4

(a) Calculated PL for HiPCo nanotubes. The dashed line shows the near-armchair direction. (b) Measured [Fig. 3(d) of Ref. 4 ] and calculated PL intensity for HiPCo samples.

Figure 5

Calculated RBM intensity in resonance with $e{h}_{11}$ for HiPCo samples [22]. The dashed line shows the near-armchair direction.