First-Principles Determination of Electron-Ion Couplings in the Warm Dense Matter Regime

We present first-principles calculations of the rate of energy exchanges between electrons and ions in nonequilibrium warm dense plasmas, liquid metals, and hot solids, a fundamental property for which various models offer diverging predictions. To this end, a Kubo relation for the electron-ion coupling parameter is introduced, which includes self-consistently the quantum, thermal, nonlinear, and strong coupling effects that coexist in materials at the confluence of solids and plasmas. Most importantly, like other Kubo relations widely used for calculating electronic conductivities, the expression can be evaluated using quantum molecular dynamics simulations. Results are presented and compared to experimental and theoretical predictions for representative materials of various electronic complexity, including aluminum, copper, iron, and nickel.

Figure 1

(a) DOS of Al with $T_i=T_e$ and Fermi-Dirac distribution (dashed lines) for three electronic temperatures at $T_e=0.1$, 1, 2 eV. Violet line is the DOS of the free-electron gas at $2.7\mathrm{g}{\mathrm{cm}}^{-3}$. Energy is measured with respect to the chemical potential $\mu (\rho ,T_e)$. (b) $G_{ei}(T_e,T_i)$ vs $T_e$ for solid density Al at $T_i=0.1\mathrm{eV}$ compared with other model predictions (see Table 1). (c) $G_{ei}(T_e,T_i)$ vs $T_e$ for Al at various densities and ionic temperatures. Vertical bar indicates the magnitude of the variation of $G_{ei}$ at melting.

Figure 2

op panels: same as Fig. 1 for Cu, Fe, and Ni at the conditions indicated in the legends. Bottom panels: $G(T_e,T_i)$ vs $T_e$ for (d) solid and liquid density Cu at $T_i=0.2\mathrm{eV}$, (e) solid density Fe at $T_i=0.156\mathrm{eV}$, and (f) solid density Ni at $T_i=0.149\mathrm{eV}$. In each case, the full lines with circles show the work’s results, the full lines without symbols are obtained using Eq. (6) with $G_0^{ei}$ set to reproduce the lowest $T_e$ value, and the long dashed lines are the results based on Eq. (5) discussed in [20]. (d) Diamonds show the experimental results of [7]; bold green segment shows the measurement of [50] for solid Cu. Inset: dashed lines indicate model predictions based on Eq. (5) presented in [20, 48]. (f) Bold green segment shows the measurement of [51].