Static and dynamic conductivity of warm dense matter within a density-functional approach: Application to aluminum and gold

The conductivity $\sigma \left(\omega \right)$ of dense Al and Au plasmas is considered where all the needed inputs are obtained from density-functional theory (DFT). These calculations involve a self-consistent determination of (i) the equation of state and the ionization balance, (ii) evaluation of the ion-ion and ion-electron pair-distribution functions, (iii) determination of the scattering amplitudes, and finally the conductivity. We present results for Al and Au for compressions 0.1–2.0, and in the temperature range $T=0.1–10\mathrm{eV}$. Excellent agreement with recent first-principles calculations using multi-ion density-functional molecular dynamics is obtained where the data fields overlap. We review first-principles approaches to the optical conductivity, including many-body perturbation theory, molecular-dynamics evaluations, and simplified time-dependent DFT. The modification to the Drude conductivity in the presence of shallow bound states in typical Al plasmas is examined and numerical results are given at the level of the Fermi Golden Rule and an approximate time-dependent DFT.

Figure 1

(Color online) Effective ionic charge $\overline{Z}$ of warm dense gold and aluminum as a function of the compression for several temperatures. The Thomas-Fermi estimates (dashed lines) at $T=10\mathrm{eV}$ and $0.1\mathrm{eV}$ are also shown.

Figure 2

(Color online) Comparison of experimental and theoretical results for the resistivity of Al plasmas. Panel (a) BSM—experimental results from Ref. 5, Benage et al., $T$ ranges from $\sim 24\text{to}1\mathrm{eV}$. Theory, Perrot and Dharma-wardana, labeled PD, Refs. 1, 2 are for the BSM range of $T$; also at $T=0.86\mathrm{eV}$ $\left({10}^3\mathrm{K}\right)$ and $2.5\mathrm{eV}$ $(\sim 3\times {10}^3\mathrm{K})$. Selected experimental data of DeSilva et al., Ref. 6 at ${10}^3\mathrm{K}$ and $3\times {10}^3\mathrm{K}$ are labeled DeSK. The DFT molecular-dynamics results of Mazevet et al., labeled MD.., are at ${10}^3\mathrm{K}$ and $3\times {10}^3\mathrm{K}$. Results from the “chemical” model of Kuhlbrot et al., KR, Ref. 27. The Thomas-Fermi model of Lee and More (LM), Ref. 15, is given only at $\sim 3\times {10}^3\mathrm{K}$. Panels (b) and (c) show the excellent agreement between the two first-principles calculations, MD and PD, in the warm dense matter range $(\rho >0.1\mathrm{g}∕{\mathrm{cm}}^3)$, at ${10}^3\mathrm{K}$ and $3\times {10}^3\mathrm{K}$, respectively.

Figure 3

(Color online) Resistivity of warm dense aluminum as a function of the compression for several temperatures.

Figure 4

(Color online) Resistivity of warm dense gold as a function of the compression for several temperatures.

Figure 5

(Color online) Ion-ion pair-distribution functions of Al from this work compared with the Car-Parinello-type simulations of Silvestrelli [56], labeled QMC. Inset: Comparison at normal density and at the melting point. Here no data from Ref. 56 are availble, but we use accurate MD simulations (Levesque et al. [57]) for comparison.

Figure 6

(Color online) Dynamic conductivity (atomic units) of Al at a compression of 0.1, i.e., $0.27\mathrm{g}∕{\mathrm{cm}}^3$ at $T=3$, 4, 6, and $10\mathrm{eV}$. Panel (a) shows the Drude conductivity and its modification by the $3s\to 3p$ bound process and the photoprocesses $3s\to k$, $3p\to k$, where $k$ indicates continuum sates. The broadening parameter $\gamma ={\gamma }_D$ is set to the value from the Drude conductivity. Panel (b) uses a fixed minimal broadening $\gamma$ of $\sim 0.08\mathrm{eV}$, at $T=3$ and $10\mathrm{eV}$. The modification of the $T=3\mathrm{eV}$ case when TDFT is used is also shown.