Strength of radial breathing mode in single-walled carbon nanotubes

Abstract

We show by ab initio calculations that the electron-phonon coupling matrix element ${\mathcal{M}}_{e\text{\ensuremath{-}}\mathit{ph}}$ of the radial breathing mode in single-walled carbon nanotubes depends strongly on tube chirality. For nanotubes of the same diameter the coupling strength ${\ensuremath{\mid}{\mathcal{M}}_{e\text{\ensuremath{-}}\mathit{ph}}\ensuremath{\mid}}^{2}$ is up to one order of magnitude stronger for zigzag tubes than for armchair tubes. For $({n}_{1},{n}_{2})$ tubes ${\mathcal{M}}_{e\text{\ensuremath{-}}\mathit{ph}}$ depends on the value of $({n}_{1}\ensuremath{-}{n}_{2})\phantom{\rule{0.3em}{0ex}}\mathrm{mod}\phantom{\rule{0.3em}{0ex}}3$, which allows us to discriminate semiconducting nanotubes with similar diameter by their Raman scattering intensity. We show measured resonance Raman profiles of the radial breathing mode which support our theoretical predictions.