Temperature dependence of plasmon resonance in single-walled carbon nanotubes

The temperature dependence of the optical response in the far-infrared (FIR) region of metallic and semiconducting rich single-walled carbon nanotubes (SWCNTs) was investigated by micro-Fourier transform infrared spectrometry with a focused beam of synchrotron radiation. The temperature dependence of the FIR spectra of both types of SWCNT showed negligibly small variations within a wide temperature range from 4 to 300 K. Upon comparison with a theoretical model for the diffusive region, it is speculated that these results might have been caused by a strong suppression of phonon scattering in relatively short CNTs with lengths of less than 1 μm.

Figure 1

(a) Schematic illustration of the experimental setup of the synchrotron facility at SPring-8. The incident light source is focused on the sample by using a Schwarzschild mirror. The measurement position is monitored by the CCD camera through the visible windows of the low-temperature cryostat. (b) Photographs of the SWCNT thin-film samples. The $M$-arc and $S$-arc samples were fabricated on the same metal plate. The measured positions are indicated by arrows in the figure.

Figure 2

(a) UV-vis-NIR absorption spectra of $M$-arc (black) and $S$-arc (red). The peaks at 700, 990, and 1825 nm correspond to the $M1,S2$, and $S1$ transitions, respectively. The absorption peaks at less than 500 nm correspond to π-plasmon excitations. (b), (c) Length distributions estimated from the AFM images of $M$-arc and $S$-arc SWCNTs on the silicon wafer. The median values estimated from the $50\%$ probabilities are indicated in the figures.

Figure 3

(a), (b) Temperature dependence of optical densities at 4–300 K. The intensities are corrected by the sample thickness estimated from the AFM observations. The lowest transition excitation peak of semiconducting SWCNTs is observed at $5500\mathrm{c}{\mathrm{m}}^{-1}$ in both samples. (c), (d) Optical densities at various wave numbers as a function of temperature. The frequencies selected here (200, 500, 1000, and $5500\mathrm{c}{\mathrm{m}}^{-1})$ are indicated as dashed lines in Figs. 3 and 3. The optical densities are almost constant in the range of 4–300 K.

Figure 4

(a) Temperature dependence of mean free path at $g_2=1.5\mathrm{eV}$. To compare the mean free path with the SWCNT length, the dashed lines indicate the maximum $L_{\mathrm{AFM}}$, as shown in Figs. 2 and 2. (b) Normalized optical densities of $M$-arc shown in Fig. 3 and numerical calculated power absorption based on Ref. [16]. The parameters are those of CNTs measured in this study.