Anomalous two-peakG′-band Raman effect in one isolated single-wall carbon nanotube

The resonant second-order $G^{\prime }$-band Raman spectra of isolated single-wall carbon nanotubes (SWNTs) exhibit an interesting resonance phenomenon, whereby the $G^{\prime }$ band for some special $\mathrm{}(n,m)\mathrm{}$ isolated SWNTs exhibits a two-peak structure, while for most SWNTs, the $G^{\prime }$-band profile is a single Lorentzian peak. The two-peak phenomenon is explained by combining the double-resonance Raman effect, originally introduced for graphite, with the singular electronic structure of SWNTs, which is unique for a given $\mathrm{}(n,m)\mathrm{}$ pair. Therefore, the $G^{\prime }$-band profile is strongly dependent on the joint density of electronic states and provides useful information about the electronic structure and on the $\mathrm{}(n,m)\mathrm{}$ assignment for the specific SWNT that is in resonance with the laser.