Nonlinear Photoluminescence Excitation Spectroscopy of Carbon Nanotubes: Exploring the Upper Density Limit of One-Dimensional Excitons

We have observed that photoemission from single-walled carbon nanotubes saturates in intensity as the excitation intensity increases. Each emission peak arising from specific-chirality tubes exhibited a saturation value independent of the excitation wavelength, suggesting an upper limit on the exciton density for each nanotube species. We developed a model based on diffusion-limited exciton-exciton annihilation, which allowed us to estimate exciton densities in the saturation regime. The estimated densities were found to be still substantially smaller than the expected Mott density.

Figure 1

Pump-intensity-dependent PL spectra. (a) Black solid curve: spectrum obtained with OPA (654 nm, 29 nJ). Red dashed curve: spectrum obtained with a cw laser diode (658 nm, $100\mu \mathrm{W}$). Inset shows that the two spectra coincide when the OPA pulse energy is very low (300 pJ). (b) Change of PL spectra versus OPA pulse energy between 1 and 30 nJ (in the order of no. 1 to no. 7). Curve 4 corresponds to the highest fluence ($\sim 1.3\times {10}^{14}\mathrm{\text{photons}}/{\mathrm{cm}}^2$).

Figure 2

Integrated PL intensity versus pump fluence for (6,5), (7,5), and (8,3) SWNTs. Pump wavelengths were 570 nm (circles), 615 nm (squares), and 654 nm (triangles). The error bars account for $\pm 5\%$. The solid curves and the dashed curves are fitting by Eq. (3, 4), respectively.

Figure 3

Evolution of PLE data with increasing pump fluence: (a) $1.2\times {10}^{12}$, (b) $1.2\times {10}^{13}$, (c) $4.1\times {10}^{13}$, and (d) $1.2\times {10}^{14}\mathrm{\text{photons}}/{\mathrm{cm}}^2$. (e)–(h) PLE spectra corresponding to (a)–(d) at PL wavelengths of 983 nm (circles), 1034 nm (squares), and 1125 nm (triangles). The magnitude of experimental error for the 1125 nm case is comparable to or slightly smaller than the size of the triangle marks.

Figure 4

Transmission spectra measured with high-fluence OPA pulses (filled circles, $1.0\times {10}^{12}\mathrm{\text{photons}}/{\mathrm{cm}}^2$; open circles, $1.0\times {10}^{14}\mathrm{\text{photons}}/{\mathrm{cm}}^2$) compared with a transmission spectrum taken with a weak cw white-light beam (dashed line).