Dynamic conductivity and partial ionization in dense fluid hydrogen

A theoretical description for optical conduction experiments in dense fluid hydrogen is presented. Different quantum statistical approaches are used to describe the mechanism of electronic transport in hydrogen's high-temperature dense phase. We show that at the onset of the metallic transition, optical conduction could be described by a strong rise in atomic polarizability, due to increased ionization, whereas in the highly degenerate limit, the Ziman weak scattering model better accounts for the observed saturation of reflectance. The inclusion of effects of partial ionization in the highly degenerate region provides great agreement with experimental results. Hydrogen's fluid metallic state is revealed to be a partially ionized free-electron plasma. Our results provide some of the first theoretical transport models that are experimentally benchmarked, as well as an important guide for future studies.

Figure 1

Bottom panel: static structure factors calculated within the Percus Yevick (P-Y) model for the range of packing fractions explored in the Ziman calculations. They correspond to densities of $1.64<r_S<1.5$. Top panel: the pair-correlation function determined from the P-Y model at $r_S=1.5$ in comparison with those calculated using ab initio methods at comparable temperatures. The dashed line is from CEIMC simulations at 1500 K [55], whereas the dotted line is from a DFT-based calculation [58]. It is worth noting that the P-Y model presented here does not capture the physics of proton pairing at lower densities, since the employed screened Coulomb potential does not account for Friedel oscillations, which dominate the pair potential at higher $r_S$.

Figure 2

Reflectance of bulk liquid metallic hydrogen versus energy shown for different models. Experimental data points are shown at 140 GPa and 2500 K for three different wavelengths from Ref. [10]. The dashed line is the calculated reflectance in the weak scattering model using the Ziman formalism and full ionization. The solid line shows a fit for a collisional frequency that is $40\%$ higher than that determined from the Ziman model, accounting for the effects of partial ionization. The dotted line represents the reflectance in the strong scattering Mott-Ioffe-Regel limit.

Figure 3

Reflectance signal of liquid metallic hydrogen in the vicinity of the metallization boundary compared to different conduction models. The experimental data from Ref. [10] are shown for two different temperatures, 1780 and 1920 K, exhibiting a non-free-electron-like energy dependence. The dotted lines represent fits using dielectric functions that include enhanced polarizibility. The solid line is the calculated reflectance within a degenerate semiconducting model assuming a band gap of 0.2 eV.

Figure 4

The ionization degree plotted as a function of temperature across the transition region from this work (squares) in comparison to the reported dissociation degree from different ab initio DFT-MD calculations. We note the definition of molecular stability and hence dissociation varies in different calculations, whereas the ionization degree is more experimentally grounded.

Figure 5

The evolution of the real part of the dielectric function across the insulator-metal transition boundary in liquid metallic hydrogen. In the highly degenerate limit (the solid line), the dielectric function was determined for the partially ionized system and is characteristic of that of the free-electron metal. Close to the onset of the transition boundary, the dielectric function (the dotted and dashed lines) does include effects of increased polarizability due to pressure ionization.