Observation of a Luttinger-liquid plasmon in metallic single-walled carbon nanotubes

Surface plasmons1, collective oscillations of conduction electrons, hold great promise for the nanoscale integration of photonics and electronics1–4. However, nanophotonic circuits based on plasmons have been significantly hampered by the difficulty in achieving broadband plasmonic waveguides that simultaneously exhibit strong spatial confinement, a high quality factor and low dispersion. Quantum plasmons, where the quantum mechanical effects of electrons play a dominant role, such as plasmons in very small metal nanoparticles5,6 and plasmons affected by tunnelling effects7, can lead to novel plasmonic phenomena in nanostructures. Here, we show that a Luttinger liquid8,9 of one-dimensional Dirac electrons in carbon nanotubes10–13 exhibits quantum plasmons that behave qualitatively differently from classical plasmon excitations. The Luttinger-liquid plasmons propagate at ‘quantized’ velocities that are independent of carrier concentration or excitation wavelength, and simultaneously exhibit extraordinary spatial confinement and high quality factor. Such Luttinger-liquid plasmons could enable novel low-loss plasmonic circuits for the subwavelength manipulation of light. Quantum-confined electrons in one dimension behave as a Luttinger liquid, a strongly correlated electronic matter distinctly different from the quasi-free electrons described by the Fermi liquid8,9. A defining characteristic of the Luttinger liquid is the spin-charge separation, where the spin and charge excitations propagate at different speeds. The elementary charge excitations of the Luttinger liquid are one-dimensional quantum plasmons, which differ substantially from their classical counterparts. Classically, plasmons are determined by the free electron density and effective mass, as in Drude conductivity, but this description completely breaks down for Luttinger-liquid plasmons, which are instead determined by the electron Fermi velocity and the number of quantum conducting channels10,11. Metallic singlewalled carbon nanotubes (SWNTs), with their extraordinary one-dimensional quantum confinement, provide the ideal platform to explore such Luttinger-liquid plasmons. Due to this strong quantum confinement, Luttinger-liquid plasmons in SWNTs with a diameter of 1 nm should persist to visible frequencies before the first intersubband transition appears14. In addition, the forbidden backscattering of Dirac electrons15,16, evidenced by ballistic transport up to micrometre lengths17–19 in metallic SWNTs, can lead to strongly confined but low-loss Luttingerliquid plasmons. The experimental observation of such Luttinger-liquid plasmons in SWNTs has remained an outstanding challenge for over a decade, although previous electrical transport and photoemission measurements have shown the presence of Luttinger liquid in SWNTs12,13,20. Here, we report the first observation of Luttinger-liquid plasmons in SWNTs using infrared scattering-type scanning nearfield optical microscopy (s-SNOM)21–23. We show that the Luttinger-liquid plasmons can be excited in a broad frequency range and that they propagate at a ‘quantized’ velocity in individual SWNTs. This velocity, unlike classical plasmon oscillations, does not depend on the free carrier density and varies only weakly with the plasmon frequency or nanotube diameter. Instead, it is mainly determined by the quantized number of conducting channels in SWNTs. At the same time, Luttinger-liquid plasmons in SWNTs simultaneously exhibit strong spatial confinement and a high-quality factor, a most sought-after feature in plasmonics24. Our observed quantum plasmon behaviour agrees quantitatively with the Luttinger-liquid theory of nanotubes. Such Luttingerliquid plasmons in SWNTs hold great potential for novel broadband plasmonic waveguides and nanophotonic circuits with low dispersion, high quality factor and strong subwavelength confinement. Metallic SWNTs with diameters ranging from 1.2 nm to 1.7 nm were grown by the arc-discharge method, and were then suspended in a micelle solution using ultrasonication, and purified to 95%metallic SWNTs using density gradient ultracentrifugation25. The nanotube solution was then spin-coated onto thin hexagonal boron nitride (hBN) flakes on SiO2/Si substrates to yield isolated individual and small bundles of SWNTs. hBN was chosen as a substrate because it is atomically flat and extremely clean, which facilitates the observation of Luttinger-liquid plasmons in the nanotubes. In contrast, it is very difficult to observe plasmon excitation in nanotubes spin-coated directly on SiO2/Si substrates. Plasmons in these metallic SWNTs were probed using infrared s-SNOM, as shown in Fig. 1a. Infrared light at 6.1 μm or 10.6 μm was focused onto the apex of a metal-coated atomic force microscope (AFM) tip with a radius of curvature of r ≈ 25 nm, the large near-field momentum of which enabled optical excitation of plasmons in the SWNTs. The excited plasmon wave propagated along the SWNT and was reflected at the nanotube end. The back-reflected plasmon wave interfered with the excitation wave under the tip, which modified the intensity of the tip-scattered infrared radiation measured by an HgCdTe detector in the far field. As the tip was scanned along the nanotube, the scattered infrared radiation varied periodically, with intensity peaks appearing at positions of constructive interference23,26,27. Figure 1b presents a representative infrared s-SNOM image of a metallic SWNT, the topography of which was recorded simultaneously (shown in the inset). Prominent plasmon oscillation