Strong Electron-Phonon and Band Structure Effects in the Optical Properties of High Pressure Metallic Hydrogen

The recent claim of having produced metallic hydrogen in the laboratory relies on measurements of optical spectra. Here, we present first-principles calculations of the reflectivity of hydrogen between 400 and 600 GPa in the $I{4}_1/amd$ crystal structure, the one predicted at these pressures, based on both time-dependent density functional and Eliashberg theories, thus, covering the optical properties from the infrared to the ultraviolet regimes. Our results show that atomic hydrogen displays an interband plasmon at around 6 eV that abruptly suppresses the reflectivity, while the large superconducting gap energy yields a sharp decrease of the reflectivity in the infrared region approximately at 120 meV. The experimentally estimated electronic scattering rates in the 0.7–3 eV range are in agreement with our theoretical estimations, which show that the huge electron-phonon interaction of the system dominates the electronic scattering in this energy range. The remarkable features in the optical spectra predicted here encourage extending the optical measurements to the infrared and ultraviolet regions as our results suggest optical measurements can potentially identify high-pressure phases of hydrogen.

Figure 1

(a) Reflectivity of $I{4}_1/amd$ hydrogen in vacuum at 50 K and 500 GPa for different impurity scattering rates both in the normal and superconducting states. The inset shows the same curves at the low energy regime along with the electron-phonon spectral function ${\alpha }^{2}F(\omega )$. (b) Ratio between superconducting and normal state reflectance of $I{4}_1/amd$ hydrogen in vacuum at 50 K and 500 GPa for different impurity scattering rates.

Figure 2

(a) Re $ϵ$, Im $ϵ$ and $-\mathrm{I}\mathrm{m}$ ${ϵ}^{-1}$ for $I{4}_1/amd$ hydrogen at 50 K and 500 GPa for ${\tau }_{\mathrm{imp}}^{-1}=200\mathrm{meV}$ in the normal state. The inset shows the same curves zoomed in the interband plasmon region. (b) Real and imaginary parts of the dielectric function of $I{4}_1/amd$ hydrogen at 50 K and 500 GPa in the IR region for ${\tau }_{\mathrm{imp}}^{-1}=200\mathrm{meV}$ in both the normal and superconducting (SC) states.

Figure 3

Electronic band structure of $I{4}_1/amd$ hydrogen at 500 GPa. Interband transitions around the $N$ point that yield a peak in Im $ϵ$ are marked with blue arrows. The DFT bands are compared to the free-electron band structure. The Fermi level is at 0 eV.

Figure 4

(a) Frequency-dependent electronic scattering rate of $I{4}_1/amd$ hydrogen at 500 GPa for different impurity scattering rates and temperatures in the region in which the experiments in Ref. [21] were performed. The same curve is also obtained for the case in which the ME formalism is not considered (curve labeled as TDDFT only). The experimental ${\tau }^{-1}=1.1\pm 0.2\mathrm{eV}$ estimate is also included [26]. The inset shows the obtained frequency dependent ${\omega }_p(\omega )$ in the same energy range, together with the ${\omega }_p^{\text{intra}}$ estimate. (b) Reflectivity of a $I{4}_1/amd$ hydrogen-diamond interface at 5 and 83 K at 500 GPa for different impurity scattering rates. Diamond IR (0.2–0.47 eV) and UV (5.47 eV electronic band gap) absorption regions are shown in shaded gray. Experimental raw values [21] are included.