# Plasmons of a Luttinger Liquid

There’s a quite remarkable experiment in a paper by the Wang group at Berkeley that recently came out in Nature Photonics demonstrating the existence of peculiar plasmons in carbon nanotubes. These are significant because this may constitute the first observations of plasmons in a Luttinger liquid. To observe these plasmons, the group used scattering-scanning near-field optical microscopy (s-SNOM).

The plasmons are novel in that they appear to have a quantized propagation velocity that depends only on the number of conducting channels. Also, the ratios for the propagation velocities appear to be in the form $1:\sqrt{2}:\sqrt{3}:\sqrt{4}$ for one, two, three and four nanotubes respectively. (Each nanotube has one conducting channel).

The plasmons are extremely well-confined spatially ($\lambda_p/\lambda \sim 1/100$, where $\lambda_p$ and $\lambda$ are the plasmon wavelength and the wavelength of free-space light respectively) and also have a quality factor of $\sim$20. This means that there may be important applications in store for these kinds of plasmons as well, though I find the result from a more fundamental perspective quite intriguing.