We study theoretically the interactions of excitonic states with surface electromagnetic modes of small-diameter (approx.<1 nm) semiconducting single-walled carbon nanotubes. We show that these interactions can result in strong exciton-surface-plasmon coupling. The exciton absorption lineshape exhibits the line (Rabi) splitting approx0.1-0.3 eV as the exciton energy is tuned to the nearest interband surface plasmon resonance of the nanotube so that the mixed strongly coupled surface plasmon-exciton excitations are formed. We discuss possible ways to bring the exciton in resonance with the surface plasmon. The exciton-plasmon Rabi splitting effect we predict here for an individual carbon nanotube is close in its magnitude to that previously reported for hybrid plasmonic nanostructures artificially fabricated of organic semiconductors deposited on metallic films. We expect this effect to open up paths to new tunable optoelectronic device applications of semiconducting carbon nanotubes.
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