Dephasing of $G$-band phonons in single-wall carbon nanotubes probed via impulsive stimulated Raman scattering

We study the coherent dynamics of G-band phonons in single-wall carbon nanotubes through impulsive stimulated Stokes and anti-Stokes Raman scattering. The probe energy dependence of the phonon amplitude as well as the preferential occurrence between Stokes and anti-Stokes components in response to chirped-pulse excitation are well explained within our model. The temperature dependence of the observed dephasing rate clearly exhibits a thermally activated component, with an activation energy that coincides with the frequency of the radial breathing mode (RBM). This fact provides a clear picture for the dephasing of G-band phonons by random frequency modulation via interaction with the RBM through anharmonicity.

Figure 1

(a) Transmitted intensity modulations due to coherent phonon oscillations in SWCNTs, which were extracted from the pump-probe signal for pump and probe energies of 1.55 eV (800 nm; $E_{\mathrm{pu}}$) and 1.48 eV (840 nm; $E_{\mathrm{pr}}$), respectively. (b) The corresponding Fourier-transformed spectrum showing radial-breathing modes (RBMs) at 6.0–7.5 THz (200–250 cm${}^{-1}$) and G-mode phonons at 47.69 THz (1590.8 cm${}^{-1}$).

Figure 2

(a) Coherent G-mode phonon dynamics measured at probe energies of 1.65 eV (750 nm), 1.57 eV (790 nm), and 1.46 eV (850 nm). The pump energy was 1.55 eV (800 nm). (b) Coherent G-mode phonon amplitude vs. probe energy, exhibiting two peaks, at 1.47 and 1.66 eV, corresponding to the SSRS and SARS processes, respectively. (c) Simulated spectral intensity for the SARS and SSRS processes obtained for a Gaussian laser spectrum centered at 1.55 eV with a spectral width of 195-meV FWHM.

Figure 3

Chirped pulse enhancing the relative amplitude of the (a) stimulated anti-Stokes Raman scattering (SARS) and (b) stimulated Stokes Raman scattering (SSRS) processes. (c) Detected G-mode phonon amplitude vs probe photon energy, normalized to the amplitude at 1.65 eV, obtained with negative dispersion [curve with (blue) triangles], transform-limited [curve with (black) squares], and positive dispersion [curve with (red) circles] pulse chirps.

Figure 4

Temperature ($T$) dependence of coherent G-mode phonons in SWCNTs measured at a probe energy of 1.65 eV (750 nm). As $T$ increases, the (a) frequency and (b) dephasing time decrease. (c) Dephasing rate vs 1/$T$. The solid (red) trace is a theoretical fit (see text). (d) Thermally activated component of dephasing. The fit [solid (red) trace] gives an activation energy of 31 meV ($=$50 cm${}^{-1}$).