Coherent nanoscale optical-phonon wave packet in graphene layers

Coherent large-wave-vector phonons in graphene layers were excited by using a 7.5-fs ultrashort laser, and observed by wavelength-resolved pump-probe transient reflectivity spectroscopy. Inter-Dirac-cone electron scattering mediated by edges and defects in graphene layers drives large-wave-vector coherent $D$-mode phonons near the Dirac point ($K$ point) of the Brillouin zone. In contrast to the normal coherent phonons generated with first-order Raman process, phonon chirp is observed, and amplitude and frequency strongly change depending on the probed wavelength. The results are discussed on the basis of doubly resonant Raman scattering process, demonstrating that generated $D$-mode coherent phonons can propagate as nanoscale optical-phonon wave packets.

Figure 1

Nanoscale optical-phonon wave packets. (a) Schematic of the inter-Dirac-cone scattering that generates large-wave-vector phonons at the graphene edge. (b) The calculated nanoscale optical phonon wave packets based on the doubly resonant Raman scattering model at $t=0$ and 0.6 ps are shown. The red and blue hexagons expand and shrink, respectively, due to the $D$-mode wave packet. Note that the unit cell changes because the wave packet consists of phonons near the Brillouin zone boundary.

Figure 2

Pump-probe reflectivity measurements. Reflectivity changes in (a) the GOS sample with 3–4 layers of graphene and (b) the Ar${}^{+}$-ion implanted HOPG (Ar-G) with an implantation dose of $3\times {10}^{13}$ ions/cm${}^2$. Schematics of the samples are shown in the insets. (c) Extracted high-frequency coherent phonons in the GOS and Ar-G samples. (d) Fourier spectra of the high-frequency coherent phonons in GOS and Ar-G.

Figure 3

The high-frequency coherent phonons. Probe-wavelength dependence of the observed spectra in (a) the GOS sample and (b) the Ar-G with the implantation dose of ${10}^{13}$ ions/cm${}^2$. The peak frequencies are indicated by circles, and the dashed lines are guides for the eyes. (c) Probe-wavelength dependence and ${\lambda }^8$ dependence (solid line) of the $D/G$ ratio of the coherent phonon amplitudes in the Ar-G. (d) Probe-wavelength dependence of the peak frequency of the GOS and Ar-G. The dashed lines are a guide for the eyes to highlight the frequency jump. (e) Schematic of the Stokes (red shaded area) and anti-Stokes (blue shaded area) signals in the wavelength-resolved coherent phonon experiment.

Figure 4

The calculation of the $D$-mode optical phonon wave packets. (a) The wave packet expected to be excited in our experiment. The dashed line and arrows show the propagation of the wave packet. The calculated $D$-mode Raman intensity at 1.9 eV (dashed line[35]) and that estimated for our coherent phonon experiment (solid line) are shown in the inset. (b) The phonon dispersion curves for the highest optical phonon mode at the $K$ point in graphene. The gray line is taken from Ref. 8, and the red line is the empirical linear dispersion used in the calculation of the wave packet. The thick red line shows the region where phonons are excited in our experiment. The electronic screening function that causes Kohn anomaly is also shown schematically above the plot. (c) The correlation between $S_{\mathrm{pump}}(x,t)$ and $S_{\mathrm{probe}}(x,0)$, which may be proportional to the coherent phonon signal. Data from the experiment (GOS exp.), calculated result (Calc.), and calculated result summed with the $G$-mode phonon response are shown. (d) Calculated and observed time dependence of the $D$-mode frequency obtained from a windowed Fourier transformation (Hanning window of 0.3 ps). The solid line is the result of the calculation. The circles and crosses are the experimental data for the GOS, and Ar-G, respectively.