Electronic Structure of Warm Dense Copper Studied by Ultrafast X-Ray Absorption Spectroscopy

We use time-resolved x-ray absorption spectroscopy to investigate the unoccupied electronic density of states of warm dense copper that is produced isochorically through the absorption of an ultrafast optical pulse. The temperature of the superheated electron-hole plasma, which ranges from 4000 to 10 000 K, was determined by comparing the measured x-ray absorption spectrum with a simulation. The electronic structure of warm dense copper is adequately described with the high temperature electronic density of state calculated by the density functional theory. The dynamics of the electron temperature is consistent with a two-temperature model, while a temperature-dependent electron-phonon coupling parameter is necessary.

Figure 1

Schematic diagram of the experiment.

Figure 2

The XAS of warm dense copper at selected times (solid curves). Spectra are displayed with an offset of $+0.8$ along the $y$ axis between time steps. For comparison, the room temperature XAS of Cu is also shown as the dotted curves.

Figure 3

Comparisons of measured and calculated XAS for (a) the ambient and (b),(c) the WDM states of Cu at selected times. (d) The DOS of solid (dotted line) and liquid (solid line) Cu and the electron distributions at the temperatures used in the modeling.

Figure 4

The temporal evolution of the $T_e$. Experimental-derived values of the $T_e$ are shown as squares. For $G_0$ and $G(T_e)$, solid lines are the $T_e$ calculated by the TTM. The shaded curves include the experimental accuracies in the $E_d$ and the temporal resolution of the detector.