Hot electron cooling in graphite: Supercollision versus hot phonon decay

Disorder-assisted electron-phonon scattering processes (supercollision processes) have been reported to dominate the cooling of hot carriers in graphene. Here, we determine to what extent this type of relaxation mechanism governs the hot carrier dynamics in the parent compound graphite. Electron temperature transients derived from time- and angle-resolved extreme ultraviolet photoemission spectra are analyzed based on a three-temperature model which considers electron gas, optical phonons, and acoustic phonons as coupled subsystems. In the probed fluence regime of $0.035–1.4\mathrm{mJ}/{\mathrm{cm}}^2$, we find no indications for supercollision processes being involved in the cooling of the hot carriers. The data are, by contrast, compatible with a hot phonon assisted mechanism involving anharmonic coupling between optical phonons and acoustic phonons, a process which has previously been suggested for graphite. We attribute the striking difference to the reported findings for (substrate-supported) graphene to the low defect density of highly ordered pyrolitic graphite.

Figure 1

Schematic illustration of potential electron-phonon coupling channels for hot carrier cooling in graphite and graphene. Supercollision (SC) scattering processes (left) allow overcoming the intrinsic momentum imbalance $q_d$ in the direct coupling between electrons and acoustic phonons (AP) with $q_{\text{AP}}$ being the AP momentum. In the hot phonon (HP) scenario (right), the coupling to the lattice involves optical phonons (OP) which decay into lower-energy APs through anharmonic coupling (green arrows).

Figure 2

Time-resolved ARPES data of HOPG for $F=0.56$ mJ/${\mathrm{cm}}^2$ near the $H$ point. (a) ARPES band map recorded with HHG light ($h\nu =$ 22.1 eV) at 100 K in equilibrium, i.e., 500 fs before excitation. (b) Brillouin zone of graphite with the energy-momentum area mapped in the experiment indicated. (c)–(e) ARPES snapshots recorded at different time delays $\mathrm{\Delta }t$ after excitation. The inset in (c) illustrates the photoexcitation from the $\pi$ to the ${\pi }^{*}$ band at $h\nu =$ 1.6 eV. A movie generated from a complete set of trARPES data is part of Ref. [24]. (f)–(h) Difference intensity maps derived from (c)–(e) in reference to the equilibrium data.

Figure 3

EDCs around $E_F$ derived from trARPES data at $F=$ 1.4 mJ/${\mathrm{cm}}^2$. (a) EDCs for different $\mathrm{\Delta }t$ in comparison to fits which assume a thermalized Fermi-Dirac distribution (solid lines). The EDCs were derived from trARPES data integrated along $k_y$ (cf. Fig. 2) and corrected as described in Ref. [24]. The corresponding raw data are shown in the inset. Photoemission intensity was integrated over a momentum window of 0.8 Å${}^{-1}$. (b), (c) Corrected EDCs for $\mathrm{\Delta }t=$ 25 and 100 fs (logarithmic scale) in comparison to the fit to illustrate the deviation from a thermalized electron distribution shortly after photoexcitation. (d) Nonthermal component of the EDCs as a function of $\mathrm{\Delta }t$: ${\tau }_1$ was estimated from the full width at $10\%$ of the maximum of a Gaussian fit to the transients.

Figure 4

(a) $T_e$ transients for $F=$ 1.4 mJ/${\mathrm{cm}}^2$ derived from FD fits to the EDCs. The red solid line is a biexponential fit to the data. The inset summarizes the characteristic time scales of electron cooling as a function of excitation fluence $F$ derived from the experimental data. ${\tau }_2$ and ${\tau }_3$ are the results of the biexponential fits to the $T_e$ transients. The black line indicates a $F^{-1/2}$ scaling as expected for ${\tau }_3$ within the SC model [21]. The blue line is the corresponding result within the HP model. (b) Experimental $T_e$ transients for different fluences in comparison to 3TM fits (dashed line: SC model; solid line: HP model).

Figure 5

Temperature dependence of the chemical potential $\mu$ derived from the FD fits. The solid line shows the calculated $T_e$ dependence under consideration of a purely metallic response of the electronic system.