Unified understanding of the electron-phonon coupling strength for nanocarbon allotropes

The electron-phonon coupling constant $\left(\lambda \right)$ of carbon nanotubes $\left(\lambda =0.006\right)$ is much smaller than that of alkali-metal-doped ${\mathrm{C}}_{60}$ crystals $\left(\lambda =0.6\right)$. This difference may be due to the shape of the $\pi$-electron conjugated system: the former has a flat, whereas the latter has a sphere. In order to confirm the shape effects in $\lambda$, we have examined the magnitude of $\lambda$ for a one-dimensional (1D) uneven peanut-shaped ${\mathrm{C}}_{60}$ polymer that has an intermediate shape of the $\pi$-electron conjugated system between a carbon nanotube and a ${\mathrm{C}}_{60}$ system, using femtosecond (fs) time-resolved pump-probe spectroscopy, because it can be expected to have an intermediate value of $\lambda$ between them. Theoretical analysis of fs-transient refractivity obtained experimentally found the magnitude of $\lambda$ of the 1D ${\mathrm{C}}_{60}$ polymer film to be 0.02 as our expectation. This indicates that the shape of the $\pi$-electron conjugated system affects the magnitude of $\lambda$ for nanocarbon allotropes significantly.

Figure 1

Schematic illustration showing the synthesis of the 1D ${\mathrm{C}}_{60}$ polymer. When the electron beam is irradiated to ${\mathrm{C}}_{60}$, two ${\mathrm{C}}_{60}$ are coalesced with each other via the GSW transformation and transformed into ${\mathrm{C}}_{120}$ isomers, followed by the synthesis of the 1D ${\mathrm{C}}_{60}$ polymer.

Figure 2

(a) The normalized reflectivity $\Delta R$ as a function of delay time $t$ of 1D ${\mathrm{C}}_{60}$ polymers at $T=40$, 100, and 270 K. The shaded areas (gray) indicate the differences from the fitting obtained at $T=270$ K. The oscillations at $t>10$ ps are due to the acoustic pulses. (b) $T$ dependence of $\tau$. The dashed line is the fits to the data using Eq. (2). The dashed-dotted line (red) is the pulse width of 120 fs.

Figure 3

The amplitudes of both $A_{\mathrm{fast}}$ (solid circle) and $C_{\mathrm{slow}}$ (solid triangle) defined in Eq. (1) as a function of temperature. The solid curves are guides to the eyes.

Figure 4

Schematic illustration of nanocarbon allotropes: two ${\mathrm{C}}_{60}$ between which are connected via (a) van der Waals interaction, (b) single C-C $\sigma$-bond, $\left(\mathrm{c}\right) 2+2$ cycloadditional bond, (d) 1D ${\mathrm{C}}_{60}$ polymer having coalesced GSW bond, and (e) single-walled CNT.