Intersubband plasmon excitations in doped carbon nanotubes

We theoretically investigate intersubband plasmon excitations in doped single wall carbon nanotubes (SWNTs) by examining the dependence of plasmon frequency on the nanotube diameter, chirality, and Fermi energy. The intersubband plasmons can be excited by light with polarization perpendicular to the nanotube axis and thus the plasmon excitations corresponds to optical transitions between the two different subbands, which are sensitive to the Fermi energy. In every SWNT, this mechanism leads to the emergence of the optical absorption peak at the plasmon frequency for a given Fermi energy, $E_F$. The plasmon frequencies calculated for many SWNTs with diameter $d_t < 2$ nm exhibit a dependence on $(1/d_t)^{0.7}$ and the frequencies are further affected by Fermi energy as $E_F^{0.25}$. With this knowledge, it is possible to develop a map of intersubband plasmon excitations in doped SWNTs that could be useful to quickly estimate the doping level and also be an alternative way to characterize nanotube chirality.