Raman resonance window of single-wall carbon nanotubes

The spectral width, or $\gamma$ value, of the Raman excitation profile for single-wall carbon nanotubes is calculated by evaluating the lifetime of the carriers. The calculated results for the $\gamma$ values are compared with the experimental spectral width of the Raman excitation profile. The $\gamma$ values evaluated by the electron-phonon interaction show a strong chirality and diameter dependence which is crucial for obtaining the peak intensities of the resonance Raman spectra. Moreover, for metallic carbon nanotubes, we expect an additional contribution to the calculated $\gamma$ values by comparing them with the experimental results. In particular, we expect that the plasmon excitation in metallic carbon nanotubes may also contribute to the spectral linewidth $\gamma$.

Figure 1

(Color online) The experimental 2D resonance Raman plot (intensity increases from blue to red) compared with resonance points calculated by the extended tight binding method presented in a Kataura plot (+ for metallic and × for semiconducting nanotubes). SDS-wrapped HiPCO carbon nanotubes in solution were used in the experiment. We can see that, for metallic nanotubes, the experimental peaks are related only to the lower transition energy compared to the extended Kataura plot. The numbers denote values of $2n+m$.

Figure 2

The RBM intensity at $310{\mathrm{cm}}^{-1}$ is plotted as a function $E_{\text{Laser}}$ for bundle SWNTs and for SDS wrapped (6,5) SWNTs in solution for (a) CoMoCAT and (b) HiPCO samples.

Figure 3

(a) Energy differences at the energy extrema between the $c_1$ and $c_2$ conduction bands. Two dashed lines indicate the iLO phonon at the $K\left(0.16\mathrm{eV}\right)$ and $\Gamma \left(0.20\mathrm{eV}\right)$ points, respectively. Filled and open circles denote type I and type II nanotubes, respectively. (b) Energy dispersion in the conduction bands $c_1$ and $c_2$. Energy bands for type I and type II $S$-SWNTs are plotted by solid lines and dashed lines, respectively. For comparing type I with type II conduction bands, we overlap these conduction bands for the two types of tubes at the $\mathbf{k}$ axis.

Figure 4

(a) Calculated $\gamma$ values for $S$-SWNTs for $0.6<d_t<1.5\mathrm{nm}$. Filled and open circles indicate type I and type II $S$-SWNTs, respectively. The $\gamma$ value for an (8,0) nanotube is near to $0\mathrm{meV}$, because of the absence of iLO phonon scattering. (b) Comparison of the calculated $\gamma$ value $\left({\gamma }_{\mathrm{TH}}\right)$ with the experimental $\gamma$ value $\left({\gamma }_{\mathrm{EX}}\right)$. Experimental $\gamma$ values were measured by plotting the RBM intensity for HiPCO-SWNTs in SDS solution at $300\mathrm{K}$ with a change of the laser energy. Filled and open circles indicate type I and type II $S$-SWNTs, respectively.

Figure 5

(a) Calculated $\gamma$ values for $M$-SWNTs in the diameter range, $0.6<d_t<1.5\mathrm{nm}$. Filled and open circles indicate $E_{11}\left(H\right)$ and $E_{11}\left(L\right)$, respectively. (b) Comparison of ${\gamma }_{\mathrm{TH}}$ with experimental ${\gamma }_{\mathrm{EX}}$ values for $M$-SWNTs.