Resonant Raman intensity of the totally symmetric phonons of single-walled carbon nanotubes

The resonant Raman intensity of the totally symmetric phonons of all single-walled carbon nanotubes in the radius range from $2.5\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}11.5\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ was calculated within a symmetry-adapted nonorthogonal tight-binding model. The obtained intensity of these modes exhibits radius and chirality dependence. The simulated Raman spectra of samples of moderate-diameter tubes with a Gaussian diameter distribution show characteristic peaks at about 1540, 1570, and $1593\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ originating from $LO$ phonons of metallic tubes, $TO$ phonons of metallic and semiconducting tubes, and $LO$ phonons of semiconducting tubes, respectively. This general behavior of the Raman spectra corresponds to that of the normally measured spectra.