Structural ( $\mathit{n},\mathit{m}$) 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 ${\omega }_{\mathrm{RBM}}$ 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 ${\gamma }_0=2.9\mathrm{}\mathrm{eV}$ and ${\omega }_{\mathrm{RBM}}=248\mathrm{}/d_t$. For example, the strong RBM intensity observed at $156{\mathrm{cm}}^{-1\mathrm{}}$ for 785 nm laser excitation is assigned to the $(13,10)$ metallic chiral nanotube on a $\mathrm{Si}/{\mathrm{SiO}}_2$ surface.