Coherent Plasmon and Phonon-Plasmon Resonances in Carbon Nanotubes

Carbon nanotubes provide a rare access point into the plasmon physics of one-dimensional electronic systems. By assembling purified nanotubes into uniformly sized arrays, we show that they support coherent plasmon resonances, that these plasmons couple to nanotube and substrate phonons, and that the resulting phonon-plasmon resonances have quality factors as high as 10. Because nanotube plasmons intensely strengthen electromagnetic fields and light-matter interactions, they provide a compelling platform for surface-enhanced spectroscopy and tunable optical devices at deep-subwavelength scales.

Figure 1

(a) Finite-length nanotubes act as plasmonic Fabry-Pérot resonators. The plasmon resonances are excited with broad-spectrum infrared light in a micro Fourier-transform infrared ($\mu$-FTIR) spectrometer. Before decaying, they can couple to phonons in the nanotube or phonons in the ${\mathrm{SiO}}_2$ substrate. (b) Scanning electron micrographs of cut and aligned nanotube segments. The nanotube film thickness is 6 nm.

Figure 2

(a) The attenuation spectra of nanotube resonators when directly resting on the ${\mathrm{SiO}}_2$ substrate, showing both plasmon (${\nu }_1$) and plasmon-coupled phonon (${\nu }_2$ and ${\nu }_3$) resonances. The spectra are sequentially vertically offset, for clarity, and the black dashed lines are fits to Fano functions. (b) Cut-direction dependence of the plasmonic absorption. The black (gray) curve is the attenuation spectrum of nanotubes cut perpendicular (parallel) to their alignment direction. Inset: polarization dependence of the intensity of peaks ${\nu }_1$ and ${\nu }_3$, with the cut direction fixed to be the perpendicular direction [as shown in Fig. 1]. The intensities of peaks ${\nu }_1$ and ${\nu }_3$ are each $6\pm 1$ times greater when the polarizer is oriented along the nanotube length rather than perpendicular to it. (c) Doping dependence of the nanotube segments. The green curve is measured immediately after ${\mathrm{NO}}_2$ exposure. For each curve below it, the samples have rested in atmospheric conditions for one extra day, whereby the doping level decreases. The sheet charge densities range from approximately ${10}^{-8}\mathrm{C}{\mathrm{cm}}^{-2}$ to ${10}^{-6}\mathrm{C}{\mathrm{cm}}^{-2}$ [20].

Figure 3

(a) The attenuation spectra of nanotube segments on the 40-nm DLC substrate, showing ${\nu }_1$ decreasing with increasing $L$ and passing through the ${1590\text{−}\mathrm{cm}}^{-1}$ nanotube phonon resonance. The spectra are sequentially vertically offset, for clarity, and the black dashed lines are fits to Fano functions, which are also offset from the data. (b) A magnification of the dashed rectangle from Fig. 3, along with fits to Fano functions (black dashed lines), showing the ${1590\text{−}\mathrm{cm}}^{-1}$ $E_{1u}$ nanotube phonons when ${\nu }_1$ is on or nearly on resonance. As $L$ increases and ${\nu }_1$ moves through the ${1590\text{−}\mathrm{cm}}^{-1}$ resonance, the character of the ${1590\text{−}\mathrm{cm}}^{-1}$ phonon resonance changes from being absent, to being an absorbing feature (due to constructive interference), to being a partially transparent feature (due to destructive interference). The fitted resonance width (${\gamma }_2$) ranges from 20 to $30{\mathrm{cm}}^{-1}$.

Figure 4

(a) The resonant frequencies, ${\nu }_1$ and ${\nu }_3$, as a function of the wave vector ($q=\pi /L$). The dashed black lines are guides to the eye. The ${\nu }_1$ frequencies derive from fits, and the ${\nu }_3$ frequencies derive from selecting the frequency corresponding to the local maximum of the attenuation spectra. Inset: ${\nu }_1$ and ${\nu }_3$ vs $q$ near the anticrossing at $1168{\mathrm{cm}}^{-1}$. The splitting between ${\nu }_1$ and ${\nu }_3$ is smaller when the DLC spacer is larger. (b) ${\gamma }_1^{-1}$, derived from fits to Eq. (1) as a function of $L$. (c) $Q$_, computed as ${\nu }_1/{\gamma }_1$, as a function of $L$. (d) The attenuation spectrum at the anticrossing ($L=180\mathrm{nm}$, $q=1.8\times {10}^5{\mathrm{cm}}^{-1}$), showing a higher $g_{13}$ splitting for the nanotubes resting on ${\mathrm{SiO}}_2$ compared to those resting on the 40-nm DLC substrate. (e) $g_{13}$ as a function of the DLC thickness ($x$).