Theory of the tangential $G$-band feature in the Raman spectra of metallic carbon nanotubes

The tangential $G$ band in the Raman spectra of a metallic single-wall carbon nanotube shows two peaks: a higher frequency component having the Lorentzian shape and a lower-frequency component of lower intensity with a Breit-Wigner-Fano (BWF) type of line shape. This interesting feature has been analyzed on the basis of phonon-plasmon coupling in a nanotube. It is shown that the low-lying optical plasmon corresponding to the tangential motion of the electrons on the nanotube surface can explain the observed features. In particular, this theory can explain the occurrence of both the Lorentzian and BWF line shapes in the $G$ band Raman spectra of metallic single-wall carbon nanotubes. Furthermore, the theory shows that the BWF peak moves to a higher frequency, has a lower intensity, and a lower half width at higher diameters of the nanotube. All these features are in agreement with experimental observations.

Figure 1

(Color online) Raman intensity of metallic carbon nanotubes as obtained from Eq. (8) for three values of the nanotube radius and with values of the parameters given in the text. The dot-dashed, solid, and dashed curves are obtained for $a∕a_B=12.5$, 14.28, and 16.66, respectively. Note the diameter dependence of the frequency, width, and height of the peak of the side band.

Figure 2

(Color online) Raman spectra of metallic carbon nanotubes with the same parameters of Fig. 1, except that here $\epsilon$ have been set to be 0. This figure allows careful examination of the diameter dependence of the FWHM of the side band.