Ultrafast electron-phonon decoupling in graphite

We report the ultrafast dynamics of the $47.4\mathrm{THz}$ coherent phonons of graphite interacting with a photoinduced nonequilibrium electron-hole plasma. Unlike conventional materials, upon photoexcitation the phonon frequency of graphite upshifts, and within a few picoseconds relaxes to the stationary value. Our first-principles density functional calculations demonstrate that the phonon stiffening stems from the light-induced decoupling of the nonadiabatic electron-phonon interaction by creating a nonequilibrium electron-hole plasma. Time-resolved vibrational spectroscopy provides a window on the ultrafast nonquilibrium electron dynamics.

Figure 1

(Color online) (a) Anisotropic reflectivity change $\Delta R_{eo}∕R$ at pump power of $50\mathrm{mW}$. The inset shows an enlargement of the trace to show the high-frequency modulation. (b) FT spectrum of the time-domain trace in (a). Inset shows the pump polarization dependence of the amplitudes of the two coherent phonons ($A_1$ and $A_2$) obtained from isotropic reflectivity $(\Delta R∕R)$ measurement. The polarization angle is measured from the plane of incidence. The probe beam is polarized at 90°. Solid and broken curves are fits to $\cos 2\theta$ function.

Figure 2

(Color online) Laser fluence dependence of the dephasing rate ${\Gamma }_2$ and the frequency ${\omega }_2$ of the coherent $E_{2g2}$ phonon obtained from a fit to an exponentially damped oscillator function. The lines are to guide the eye. Inset shows the Brillouin zone of graphite.

Figure 3

(Color online) Time evolution of the $E_{2g2}$ phonon frequency, obtained from time-windowed FT, for different laser fluences. The widths of the Gaussian time windows are $80\mathrm{fs}$ for $t<0.4\mathrm{ps}$, $300\mathrm{fs}$ for $0.4<t<2\mathrm{ps}$, and $800\mathrm{fs}$ for $t\ge 2\mathrm{ps}$.

Figure 4

(Color online) Calculated $E_{2g2}$ frequency change as a function of the excitation charge density for the AED (square), NTD (triangle), TD (filled circle), and ID (open circle). The top axis shows the corresponding electronic temperature $T_e$ for TD. Arrows show schematically the excitation and relaxation pathways for the $e\text{−}h$ distribution: (A) quasi-instantaneous excitation by a laser pulse, (B) deexcitation within $<100\mathrm{fs}$ through the creation of secondary $e\text{−}h$ pairs around the Fermi level $E_F$, (C) thermalization of the $e\text{−}h$ plasma in $\sim 0.2\mathrm{ps}$, and (D) cooling down of the $e\text{−}h$ plasma in $\sim 2\mathrm{ps}$ through optical phonon emission. Ultrafast phonon stiffening is ascribed to steps A and B. The highest density excitation (fluence of $1\mathrm{mJ}∕{\mathrm{cm}}^2$) in our experiment corresponds to $5.8\times {10}^{20}\text{electron}\text{−}\text{hole}\text{pairs}∕{\mathrm{cm}}^3$ or 0.005 electrons/atom.