Interplay between excitons and plasmons We study excited states of doped carbon nanotubes and narrow-gap semiconductor carbon nanotubes. In the optical response of these nanotubes, it is revealed that excitons, which are bound states of photo-excited electrons and holes, and plasmons, which are collective charge excitations, play important roles. For example, narrow-gap semiconductor nanotubes, which have typically small energy gap of about 10 meV, exhibit peaks of optical absorption spectra in the far-infrared region. We revealed that these peaks can come from excitons for long nanotubes and from plasmons for short nanotubes. This is due to the fact that an exciton which contributes to strong optical absorption crosses over to a plasmon as the wave vector increases. Wave-vector dependence of excited states of narrow-gap (18, 0) nanotube. A hatched region indicates one-particle excitation continuum, dotted lines indicate excitons, and a solid line denotes a plasmon. Colors on the background indicate the real part of the dynamical conductivity, which characterizes optical absorption. The energy of the lowest exciton at zero wave vector increases with the wave vector, is immersed into the continuum at a wave vector denoted by an arrow, and is changed to be a plasmon. A dotted-dashed line denotes an analytic energy dispersion relation of the plasmon in the long-wave-length limit. Back
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