Dependence of Raman spectra $G^{\prime }$ band intensity on metallicity of single-wall carbon nanotubes

We report the peculiar behavior of the $G^{\prime }$ band Raman intensity, which is dependent on the metallicity of single-wall carbon nanotubes (SWCNTs). In the metallic SWCNTs, the $G^{\prime }$ band intensity was enhanced relative to the $G$ band intensity, while the $G^{\prime }$ band intensity was suppressed in the semiconducting SWCNTs. Resonance Raman spectroscopy (using laser energies of $E_{\mathit{\text{laser}}}=2.41$, 1.96, 1.58, and $1.165\mathrm{eV}$) showed these features on the metal-enriched and semiconducting-enriched SWCNT samples that had been selectively separated by the nitronium ions. The metallicity dependence was explained theoretically by calculating the resonance Raman intensity within the extended tight-binding calculations. The calculated results confirm that the $G^{\prime }$ band intensity of the metallic SWCNTs is stronger than that for the semiconducting SWCNTs because the electron-phonon matrix elements for the TO phonon at the $K$ point is larger for metallic SWCNTs and the resonance window for $E_{33}^S$ is larger than that for $E_{11}^M$.

Figure 1

(Color online) Raman spectra at various excitation energies of the SWCNT sample: (a) $2.41\mathrm{eV}$, (b) $1.96\mathrm{eV}$, (c) $1.58\mathrm{eV}$, and (d) $1.165\mathrm{eV}$. All Raman spectra were normalized to the $G$ band intensity. The inset in each figure is the enlarged radial breathing mode. The numbers in each figure are the diameters of the corresponding peaks in nm (upper axis) and phonon frequencies (bottom axis). $E_{ii}^{S\left(M\right)}$ indicate the van Hove singularity transition energy between the $i\text{th}$ levels of the semiconducting (metallic) SWCNT. (e) Kataura plot obtained from extended tight-binding model. The solid and dashed lines are incident laser energies and the corresponding scattered energies used in our experiment. The arrows indicate the scattered photons of the corresponding peaks of (a)–(c). The green, yellow, and red vertical lines are positions of main RBM peak in (a), (b), and (c), respectively.

Figure 2

(Color online) Raman spectra of (bottom) the pristine HiPCO sample and (top) the NHFA-treated HiPCO sample at excitation energies of [(a)–(c)] $2.41\mathrm{eV}$, [(d)–(f)] $1.96\mathrm{eV}$, and [(g)–(i)] $1.58\mathrm{eV}$. The notations are the same as shown in Fig. 1.

Figure 3

(Color online) Raman spectra of the acid-treated HiPCO samples: pristine (bottom), for $12\mathrm{h}$ (middle), and for $48\mathrm{h}$ (top) at excitation energies of [(a)–(c)] $2.41\mathrm{eV}$ and [(d)–(f)] $1.58\mathrm{eV}$. The notations are the same as shown in Fig. 1.

Figure 4

(Color online) The calculated $G^{\prime }$ band Raman intensity as a function of (a) Raman shift and (b) laser excitation energy for iTO overtone. (c) and (d) are plotted as a function of the Raman shift and laser excitation energy for the iLO overtone, respectively. The blank and black filled circles indicate the lower $E_{11}^M$ transition $\left(E_{11}^{\mathrm{LM}}\right)$ and the higher $E_{11}^M$ transition $\left(E_{11}^{\mathrm{HM}}\right)$, respectively. (e) The resonance window, $\gamma$ value, as function of the excitation laser energy. The blue and red filled circles indicate the $E_{22}^S$ and $E_{33}^S$ transitions, respectively.