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 2.50.3em0ex0.3em0exto0.3em0ex11.50.3em0ex 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 15930.3em0excm^-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.