Phonon Softening in Individual Metallic Carbon Nanotubes due to the Kohn Anomaly

We have studied the line shape and frequency of the $G$ band Raman modes in individual metallic single walled carbon nanotubes (M-SWNTs) as a function of Fermi level (${ϵ}_F$) position, by tuning a polymer electrolyte gate. Our study focuses on the data from M-SWNTs where explicit assignment of the $G^{-}$ and $G^{+}$ peaks can be made. The frequency and line shape of the $G^{-}$ peak in the Raman spectrum of M-SWNTs is very sensitive to the position of the Fermi level. Within $\pm \hslash \omega /2$ (where $\hslash \omega$ is the phonon energy) around the band crossing point, the $G^{-}$ mode is softened and broadened. In contrast, as the Fermi level is tuned away from the band crossing point, a semiconductinglike $G$ band line shape is recovered both in terms of frequency and linewidth. Our results confirm the predicted softening of the $A$-symmetry LO phonon mode frequency due to a Kohn anomaly in M-SWNTs.

Figure 1

(a) Schematic diagram of the experimental setup. The excitation laser shines through the $\mathrm{PEO}/{\mathrm{LiClO}}_4$ polymer electrolyte. (b) An AFM image indicating that the nanotubes are spaced out and are typically isolated from one another.

Figure 2

(a) $G$ band intensity map vs applied gate voltage $V_G$ for an individual M-SWNT. (b) $G$ band spectrum, for the same nanotube as in (a), taken at the indicated $V_G$ values. The spectrum at the bottom of the panel corresponds to $V_{G,o}$. (c) $G$ band of a M-SWNT whose peaks are difficult to track because the spectrum is composed of many overlapping peaks. Arrows indicate peaks associated with the electrolyte (d) $G$ band of a S-SWNT taken at the different $V_G$, with a step in $V_G$ of 0.2 V between traces.

Figure 3

(a) Frequency of $\mathrm{M}\mathrm{\text{−}}{G}^{+}$ (open points) and $\mathrm{M}\mathrm{\text{−}}{G}^{-}$ (filled points), (b) linewidth ${\Gamma }_{\mathrm{EPC}}$ of $\mathrm{M}\mathrm{\text{−}}{G}^{-}$, and (c) $-1/q$ of $\mathrm{M}\mathrm{\text{−}}{G}^{-}$ as a function of the Fermi level for two M-SWNT [tube 1 dots, tube 2 triangles]. ${\Gamma }_0$ is taken as $12$ and $10{\mathrm{cm}}^{-1}$ for tubes 1 and 2, respectively. The solid lines in (a) and (b) are the calculated frequencies ($T=0\mathrm{K}$) and linewidths ($T=300\mathrm{K}$) of the LO $A$ symmetry phonon from Ref. 11.