Finite-temperature density-functional-theory investigation on the nonequilibrium transient warm-dense-matter state created by laser excitation

We present a finite-temperature density-functional-theory investigation of the nonequilibrium transient electronic structure of warm dense Li, Al, Cu, and Au created by laser excitation. Photons excite electrons either from the inner shell orbitals or from the valence bands according to the photon energy, and give rise to isochoric heating of the sample. Localized states related to the $3d$ orbital are observed for Cu when the hole lies in the inner shell $3s$ orbital. The electrical conductivity for these materials at nonequilibrium states is calculated using the Kubo-Greenwood formula. The change of the electrical conductivity, compared to the equilibrium state, is different for the case of holes in inner shell orbitals or the valence band. This is attributed to the competition of two factors: the shift of the orbital energies due to reduced screening of core electrons, and the increase of chemical potential due to the excitation of electrons. The finite-temperature effect of both the electrons and the ions on the electrical conductivity is discussed in detail. This work is helpful to better understand the physics of laser excitation experiments of warm dense matter.

Figure 1

Density of states of (a) BCC Li, (b) FCC Al, and (c) FCC Cu with a perfect lattice structure at ambient condition. The black solid lines show the calculated DOS with the occupied DOS shown as shades. The positions of their chemical potentials are marked with the vertical dashed black lines and labeled in the legends. The red lines represent the same quantity as the black lines but are calculated with 10 electrons removed from the inner shell orbitals ($1s$ for Li, $2s$ for Al, and $3s$ for Cu). For the blue lines, the number of such holes is increased to 32. For a better display, the DOS for the inner shell orbitals and for the valence band use different scales corresponding to the left and right axes.

Figure 2

LDOS of Li, Al, and Cu with perfect lattice structure at room temperature calculated with 10 atoms having a hole in their inner shells. (a) LDOS of BCC Li of atoms with (red color) and without (black color) a hole in the $1s$ orbital. (b) LDOS of FCC Al of atoms with (red color) and without (black color) a hole in the $2s$ orbital. (c) LDOS of FCC Cu of atoms with (red color) and without (black color) a hole in the $3s$ orbital. The LDOS for the inner shell orbitals and for the valence band are shown with different scales (left and right axis, respectively) for better display.

Figure 3

Density of states of (a) Cu and (b) Au with perfect lattice structure at room temperature. As in Fig. 1, the black solid lines show the calculated DOS, while the shaded area shows the corresponding occupied DOS. The positions of the chemical potential are marked with the vertical dashed lines and are labeled in the legend. The red (blue) lines represent the same quantity as the black lines but are calculated with 10 (32) electrons removed from their valence bands ($3d$ for Cu and $5d$ for Au).

Figure 4

Calculated real part of electrical conductivity of Li, Al, and Cu placed in their perfect lattice structures at room temperature with variable number of holes in their inner shells. Experimental measurements are plotted as purple dots for comparison. Inset: Zoom-in of the DC limit. (a) Li: the black line corresponds to the case without holes, while the red and blue lines represent the ones with 10 and 32 atoms having an electron removed from the 1s orbital, respectively. (b) The same for Al: the red and blue lines correspond to the cases of 10 and 32 atoms having an electron removed from the $2s$ orbital, respectively. (c) The same for Cu: the red and blue lines correspond to the cases with 10 and 32 atoms having an electron removed from the $3s$ orbital, respectively. Experimental data are marked with purple dots [66, 67, 68].

Figure 5

Calculated real part of the electrical conductivity of Cu and Au placed in their perfect lattice structures at room temperature with variable number of holes in their valence bands. Experimental measurements are plotted as purple dots for comparison [68, 69]. Inset: Zoom into the DC limit. (a) Cu: the black line represents the AC conductivity without holes, while the red (blue) line represents the one with 10 holes (32 holes) in the $3d$ orbital. (b) The same for Au: red (blue) line represents the case with 10 (32) holes in the $5d$ orbital.

Figure 6

Real part of the electrical conductivity of FCC Cu at an electron temperature of 1 eV with variable number of holes in the inner shell. Black line: no holes; red (blue) line: 10 (32) electrons removed from the $3s$ orbital, resulting in 10 (32) atoms having one hole. Inset: zoom into the static limit.

Figure 7

Same as Fig 6, but for the case that the holes are created in the valence band. The holes are not bounded to specific atoms in this case.

Figure 8

Finite-temperature effect of the exchange-correlation potential on the electrical conductivity of FCC Cu at an electronic temperature of 1 eV. Blue curve: finite-temperature exchange-correlation functional based on the GDSMFB parametrization [57]. Red curve: zero-temperature functional with the Perdew-Zunger (PZ) parametrization [56].

Figure 9

Effect of the ionic structure on the electrical conductivity of Cu at $T=1$ eV. Red: FCC Cu at an electronic temperature of 1 eV. Blue: Cu with a temperature of 1 eV for both ions and electrons. The error bars are smaller than the line width. The electrical conductivity of Cu at 300 K [the same as the black line in Fig. 5] is also plotted as a black line for reference.