Strongly Coupled Optical Phonons in the Ultrafast Dynamics of the Electronic Energy and Current Relaxation in Graphite

Ultrafast charge carrier dynamics in graphite has been investigated by time-resolved terahertz spectroscopy. Analysis of the transient dielectric function and model calculations show that more than 90% of the initially deposited excitation energy is transferred to a few strongly coupled lattice vibrations within 500 fs. These hot optical phonons also substantially contribute to the striking increase of the Drude relaxation rate observed during the first picosecond after photoexcitation. The subsequent cooling of the hot phonons yields a lifetime estimate of 7 ps for these modes.

Figure 1

(a) THz waveform $E_0(t)$ transmitted through unexcited graphite and the pump-induced changes $\Delta E_{\tau }(t)$ at $\tau =0.5\mathrm{ps}$. (b) Change in the THz electric field at $t=-12\mathrm{fs}$ as a function of the pump-probe delay $\tau$. (c) Pump-induced changes $\Delta {\epsilon }_{\tau }$ of the in-plane dielectric function of graphite at $\tau =0.5\mathrm{ps}$ after photoexcitation. Thick solid lines are model fits (see text). (d) Magnified section of the imaginary part of $\Delta {\epsilon }_{0.5\mathrm{ps}}$ with model fit and respective contributions of direct and indirect optical transitions.

Figure 2

(a) Sketch of the in-plane band structure of graphite close to the $K$ or $K^{\prime }$ point where valence and conduction band slightly overlap. Arrows indicate possible direct and indirect optical transitions induced by the probe pulse. (b) Brillouin zone perpendicular to the $c$ axis. The Fermi surface is located around the $K$ and $K^{\prime }$ points. Arrows mark possible scattering events of electrons and correspond to wave vector changes $\Delta \mathit{k}$ that are confined to the vicinity of the $\Gamma$ and $K$ points.

Figure 3

(a) Temporal evolution of electronic temperature $T_e$. The dashed line indicates the hypothetical $T_e$ decay if only cold SCOPs were involved; the solid line marks an exponential decay with a time constant of 7 ps. (b) Temporal evolution of the Drude relaxation rate $\gamma$. (c) Pump-induced change $\hslash \Delta {\omega }_{\mathrm{pl}}$ in the unscreened plasma frequency vs electronic temperature. The solid line is a theoretical prediction. (d) Pump-induced changes $\Delta \gamma (\tau )$ vs $T_e(\tau )$ together with the calculated contribution due to hot SCOPs (solid line).