A scattering scanning near-field optical microscope is an instrument based AFM which could be used to investigate nano-structure. By exploiting the near-field electromagnetic waves in the vincinty of the AFM tip to image the object, SNOM breaks the Abbe diffraction limit of one half wavelength (~λ, for visible light ~500nm) with a resolution approximately equal to the radius of the tip (~10nm).

Fig1 : The schematic diagram of s-SNOM. (F. Keilmann et al., Phil. Trans. R. Soc., 362, 787-805, 2004.)

The schematic diagram of s-SNOM is shown in Fig1. A foucused beam light is shed on the AFM tip, the illumintaed tip exhibits enhanced optical fields in its neighborhood. After interplaying with the local region of the sample being detected, the scattered light carrying the information of the sample is measured by the detector in the far field. As the AFM tip oscillates at the cantilever's mechanical resonance frequency Ω, the light scattered by the tip could be yanked out from the background through a lock-in amplifier.

Zhiwen Shi et al. first reported the observation of Luttinger liquid plasmons in metallic single-walled carbon nanotubes with s-SNOM and their work was published in Nature Photonics. Link

Luttinger liquid is a theoretical model describing interacting electrons (or other fermions) in a one-dimensional conductor. For electron gas in metal, there are many different models which could give the truth to the different extent according to their assumptions. For instance, in the elementary Drude model, the outer electron are itinerant and are considered as classical ideal(non-interacting) gas. This simple classical Drude model provides a very good explanation of DC and AC conductivity in metals. The Drude-Sommerfeld model went a “quantum leap” by substituting the Maxwell-Boltzmann distribution with Fermi-Dirac distribution, but it is still non-interacting. Landau–Fermi liquid theory is a theoretical model considering interaction that describes the normal state of most metals at sufficiently low temperatures