Logarithm Diameter Scaling and Carrier Density Independence of One-Dimensional Luttinger Liquid Plasmon

Quantum-confined electrons in one-dimensional (1D) metals are described by a Luttinger liquid. The collective charge excitations (i.e., plasmons) in a Luttinger liquid can behave qualitatively different from their conventional counterparts. For example, the Luttinger liquid plasmon velocity is uniquely determined by the electron-electron interaction, which scales logarithmly with the diameter of the 1D material. In addition, the Luttinger liquid plasmon is predicted to be independent of the carrier concentration. Here, we report the observation of such unusual Luttinger liquid plasmon behaviors in metallic single-walled carbon nanotubes, a model system featuring strong electron quantum confinement. We systematically investigate the plasmon propagation in over 30 metallic carbon nanotubes of different diameters using infrared nanoscopy. We establish that the plasmon velocity has a weak logarithm dependence on the nanotube diameter, as predicted by the Luttinger liquid theory. We further study the plasmon excitation as a function of the carrier density in electrostatically gated metallic carbon nanotubes and demonstrate that the plasmon velocity is completely independent of the carrier density. These behaviors are in striking contrast to conventional plasmons in 1D metallic shells, where the plasmon dispersion changes dramatically with the metal electron density and the 1D diameter. The unusual behaviors of Luttinger liquid plasmon may enable novel nanophotonic applications based on carbon nanotubes.