Structural (n,m) Determination of Isolated Single-Wall Carbon Nanotubes by Resonant Raman Scattering
We show that the Raman scattering technique can give complete structural information for one-dimensional systems, such as carbon nanotubes. Resonant confocal micro-Raman spectroscopy of an $(n,m)$ individual single-wall nanotube makes it possible to assign its chirality uniquely by measuring one radial breathing mode frequency ${\ensuremath{\omega}}_{\mathrm{RBM}}$ and using the theory of resonant transitions. A unique chirality assignment can be made for both metallic and semiconducting nanotubes of diameter ${d}_{t}$, using the parameters ${\ensuremath{\gamma}}_{0}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2.9\mathrm{eV}$ and ${\ensuremath{\omega}}_{\mathrm{RBM}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}248/{d}_{t}$. For example, the strong RBM intensity observed at $156{\mathrm{cm}}^{\ensuremath{-}1}$ for 785 nm laser excitation is assigned to the $(13,10)$ metallic chiral nanotube on a $\mathrm{Si}/{\mathrm{SiO}}_{2}$ surface.