Spectroscopy of zigzag single-walled carbon nanotubes: Comparing femtosecond transient absorption spectra with ab initio calculations

Femtosecond transient absorption spectroscopy was applied to map out the electronic transition energies of a selected semiconducting zigzag carbon nanotube, the (11,0) tube. The experiment was performed by resonant excitation of the lowest electronic transition with spectrally narrow pump pulses, ensuring predominant selection of the desired tube type from a mixture of various species. We found that the lowest and the second electronic transitions are characterized by induced transmission bands peaking at 1042 and $741\mathrm{nm}$, respectively. The association of the resolved spectral bands to the two lowest electronic transitions of the (11,0) tube was further verified by examining the corresponding kinetic profiles. Results of ab initio calculations are also presented for comparing the transition energies and for explaining the transient absorption kinetics detected at different wavelengths.

Figure 1

Energy diagrams of the excitonic states of the (11,0) tube obtained by ab initio calculations. The numbers denote the principal numbers, $u$ and $g$ represent odd and even symmetry, respectively. The right-handed panel shows an expanded view of the subgroup corresponding to the $n=0$ level; the optically allowed and dark states are depicted by solid and dashed lines, respectively. The ${}_{0}A_0^{-}$ state is referred to as the $E_1$ state in the experimental portion of this paper.

Figure 2

The TA spectrum recorded with spectrally wide pulses centered at $1037\mathrm{nm}$ at a delay time of $70\mathrm{fs}$. The three Gaussian components resulting from spectral deconvolution are shown in dashed lines and the fit is given by the solid line. The shaded area shows the Gaussian band associated with the (11,0) and/or (8,1) tubes.

Figure 3

The TA spectra measured in the spectral region corresponding to the $E_1$ and $E_2$ transitions of the (11,0) tube upon excitation at $1040\mathrm{nm}$ with spectrally narrow pump pulses. The spectral was recorded at a delay time of $190\mathrm{fs}$ with a pump fluence of $4.73\times {10}^{13}\text{photons}∕\text{pulse}{\mathrm{cm}}^2$. The solid line drawn over the experimental data collected at shorter wavelength represents a Gaussian fit. Deconvolution of the spectrum obtained at longer wavelength results in two Gaussian components (dashed and dotted lines), and the solid line is the fit of the spectrum. The vertical dashed line indicates the center frequency of the pump pulses and the horizontal dotted line is the baseline of the spectra $(\Delta \mathrm{OD}=0)$.

Figure 4

The change of the maximum amplitude of the transient absorption kinetics at $740\mathrm{nm}$ (circles) and $1040\mathrm{nm}$ (squares) with the intensity of pump pulses at $1040\mathrm{nm}$, plotted as a function of the intensity (circles vs bottom axis) or its square root (squares, top axis). The dashed lines represent the linear fits of the data.

Figure 5

(a) The TA kinetics probed at $1040\mathrm{nm}$ at different pump pulse intensities (in $\text{photons}∕\text{pulse}{\mathrm{cm}}^2$) at $1040\mathrm{nm}$. The kinetics are scaled to an equal amplitude at $3\mathrm{ps}$. (b) The TA kinetics probed at $740\mathrm{nm}$ at two different intensities of $1040\mathrm{nm}$ pump pulse. The kinetics are normalized at the signal maxima.

Figure 6

Comparison of the kinetics probed at 740 (circles) and $1040\mathrm{nm}$ (solid line) upon resonant excitation with spectrally narrow pulses centered at $1040\mathrm{nm}$. The data were collected with a pump fluence of $3.85\times {10}^{13}$ and $8.20\times {10}^{12}\text{photons}∕\text{pulse}{\mathrm{cm}}^2$, respectively. The kinetics are normalized at the signal maxima.

Figure 7

Comparison of the TA kinetics at 1020 (open circles) and $1040\mathrm{nm}$ (squares) measured at a pump intensity of $4.30\times {10}^{12}\text{photons}∕\text{pulse}{\mathrm{cm}}^2$. For ease of comparison, the data collected at $1040\mathrm{nm}$ are multiplied by $(-1)$ and are scaled to equal amplitude at $3\mathrm{ps}$ to the kinetics measured at $1020\mathrm{nm}$. The solid lines are the results of global fitting. See text for details.