Length-dependent plasmon resonance in single-walled carbon nanotubes

The optical response of single-walled carbon nanotubes (SWCNTs) to far-infrared (FIR) radiation was systematically studied using various SWCNTs with different tube-length distributions. The observed peak position in the FIR spectra linearly scaled with the inverse of tube length irrespective of diameter, which is consistent with the dispersion relation predicted by the one-dimensional plasmon resonance model. The effects of chemical doping on the FIR spectra of the separated metallic and semiconducting SWCNTs clearly indicate that the motion of plasmons in the electronic band structures is primarily responsible for the optical response in these spectral regions. The observed absorption peaks are naturally sensitive to the presence of defects on the tube wall and correlated with the electric resistance, suggesting that the plasmons resonate with the current path length of the SWCNTs.