Near field optical microscopy of Luttinger liquid plasmons in single walled carbon nanotubes

Quantum-confined electrons in one dimension (1D) behave as Luttinger liquid, which features charge spin separation and other intriguing properties in dramatic contrast to Fermi liquid. The strong electron electron interaction in Luttinger liquid dominates its properties and is characterized by a single Luttinger liquid parameter. Metallic single walled carbon nanotubes (SWNTs) is one of the best candidates to explore such Luttinger-liquid physics. Recently developed scanning near field optical microscopy (SNOM) has made it possible to extract this Luttinger liquid parameter quantitatively from its plasmon wavelength by a single scanning. With this quantitative information enabled by SNOM, we performed systematic study of this Luttinger liquid plasmons and how they are modified by extrinsic factors. This study provides more fundamental understanding of Luttinger liquid behaviours in carbon nanotubes and also facilitates the applications of nanophotonic devices based on remarkably confined and high quality factor carbon nanotube plasmons.