Attosecond Soft X-Ray Spectroscopy Reveals Energy Flow in a Semimetal

We show that core-level x-ray absorption near edge structure (XANES) spectroscopy with attosecond soft x-ray (SXR) pulses [1] can image the flow of energy inside a material in real time [2]. We photoexcite graphite with a $11\pm 1$ fs pump pulse at 1850 nm, or with a $15\pm 1$ fs pulse at 800 nm, for various pump fluences between $2.8 \pm$ 0.2 $\text{mJ}/\text{cm}2$ and $81\pm 5 \ \text{mJ}/\text{cm}2$ . Figure 1(a) shows the measured differential x-ray absorption $\Delta\mathrm{A}(\mathrm{E})$ (pumped minus unpumped) from which striking changes of up to 15% are immediately apparent. We identify these features as $\pi$ bonding state and as $\pi^{*}$ and $\sigma^{*}$ antibonding states. Attosecond-resolved measurement with a pump-probe delay step size of 0.6 fs show the buildup of coherent charge oscillations, i.e., polarization of the material. These oscillations occur at occupied states below and unoccupied states above the Fermi level predominantly at the pump carrier frequency. We identify the incoherent background due to the dephasing of coherent charge oscillation. This background rises within a few oscillations of the light field, signifying the ultrafast transfer of energy from the light field into the electron and hole excitation of the material. We find that ultrafast dephasing of the coherent carrier dynamics is governed by impact excitation (lE) for electrons, while holes exhibit a switchover from impact excitation to Auger heating (AH) already during the 11-fs duration of the infrared light field. We further analyze the coherent phonon signal by analyzing the oscillatory pattern exhibited by the $\sigma^{*}$ data with a short-time Fourier transform (STFT) analysis This analysis shows that already during and shortly after the laser excitation, coherent motion emerges over a broad range of frequencies. A comparison with the phonon dispersion from two-temperature-model molecular dynamics (TTM MD) simulations [4] [Fig. $1(\mathrm{e})]$ identifies them as the Raman-active $\ulcorner-\mathrm{E}2\mathrm{g}$ and the non-Raman-active K - A'1 SCOPs at $46.4\pm 2.7$ and 42.7 $\pm 1.1$ THz, respectively. The surprising early contribution from the (non-Raman-active) $\mathrm{A}^{\prime}1$ mode originate from the very strong electron-SCOPs coupling, thus acting almost impulsively.