Softening of the Radial Breathing Mode in Metallic Carbon Nanotubes

In this work, the Fermi level $(\epsilon_{\rm F})$ dependence of the radial breathing mode (RBM) of metallic single walled carbon nanotubes (M-SWNTs) has been investigated. In situ Raman spectra were obtained from several individual M-SWNTs while varying $\epsilon_{\rm F}$ electrochemically. The RBM frequency of an intrinsic M-SWNT is shown to be downshifted relative to highly doped tubes by $\sim2{\rm cm}^{-1}$. The downshift is greatest for small diameter and small chiral angle nanotubes. Most tubes do not show any change in RBM linewidth. A comparison is drawn between the RBM and the G-band ($A_{\rm LO}$ phonon) with respect to the $\epsilon_{\rm F}$ dependence of their frequencies and linewidths.