Ultrafast Formation of a Fermi-Dirac Distributed Electron Gas

Time- and angle-resolved photoelectron spectroscopy with 13 fs temporal resolution is used to follow the different stages in the formation of a Fermi-Dirac distributed electron gas in graphite after absorption of an intense 7 fs laser pulse. Within the first 50 fs after excitation, a sequence of time frames is resolved that are characterized by different energy and momentum exchange processes among the involved photonic, electronic, and phononic degrees of freedom. The results reveal experimentally the complexity of the transition from a nascent nonthermal towards a thermal electron distribution due to the different timescales associated with the involved interaction processes.

Figure 1

(a) WL-pump and XUV-probe cross-correlation signal of the experiment. For details see Refs. [21, 24]. (b) Schematic of time-resolved pump-probe ARPES of HOPG. Pump pulses are polarized along the $x$ direction. The entrance slit of the electron analyzer is aligned along the $y$ direction. (c) Top: illustration of the Brillouin zone of HOPG. Bottom: closeup of the Brillouin zone (BZ) around the $H$ point (gray) with the momentum cut probed in the experiment indicated (black). The red dashed line marks the constant-energy contour of the ${\pi }^{*}$ band near $E-E_F=0.8\mathrm{eV}$. Areas of primary excitation are highlighted in yellow.

Figure 2

Time-resolved ARPES data of HOPG taken near $H$ for excitation with 7 fs pump pulses ($F=1.7\mathrm{mJ}/{\mathrm{cm}}^2$). (a)–(d) ARPES snapshots recorded at different time delays $\mathrm{\Delta }t$. (e) Illustration of the photoexcitation process. (f)–(h) EDCs around $E_F$ for different $\mathrm{\Delta }t$ derived from the trARPES data. Photoemission intensity was integrated over a momentum window of $0.8{\AA }^{-1}$. Dashed lines are fits of a FD distribution to the EDCs. The inset underneath (f) indicates the pump-pulse spectrum (logarithmic scale) convolved with the energy resolution of the trARPES experiment and mapped onto the energy axis according to the excitation process illustrated in (e). Momentum-resolved photoemission intensity transients are for reference added to the Supplemental Material [24].

Figure 3

Analysis of trARPES data for $F=1.7\mathrm{mJ}/{\mathrm{cm}}^2$. (a) $E_{{\pi }^{*}}$ as a function of $T_{\mathrm{FD}}$. Time markers (blue diamonds) separate the different stages of thermalization identified in (b). Data are normalized to $E_{{\pi }^{*}}$ for $\mathrm{\Delta }t=8\mathrm{fs}$. Error bars indicate exemplary uncertainties in $T_{\mathrm{FD}}$. The solid line is a result of a calculation for a FD distributed electron gas. (b) $\mathrm{\Delta }{E}_{{\pi }^{*}}$ as a function of $T_{\mathrm{FD}}$. Arrows indicate the direction of time evolution and different stages in the thermalization process. Similar results for $F=0.9\mathrm{mJ}/{\mathrm{cm}}^2$ are compiled in the Supplemental Material [24]. (c) Spectrally resolved evolution of the ${\pi }^{*}$ band occupations before, during, and after stage III: difference between experimental EDCs and a FD distributed electron gas for $T=5500\mathrm{K}$. Data sets and zero lines are partly offset for clarity. Data for $\mathrm{\Delta }t=8\mathrm{fs}$ are scaled by a factor of 0.5. Experimental EDCs including fits are for reference added to the Supplemental Material [24].

Figure 4

Stages of thermalization and characteristic timescales of energy and momentum exchange processes. Relevant interaction processes are indicated. Time markers separating the stages result from the evaluation of the experimental data for $F=0.9$ and $F=1.7\mathrm{mJ}/{\mathrm{cm}}^2$. Widths of the markers account for the experimental uncertainty.