Strong electron-phonon and band structure effects in the optical properties of high pressure metallic hydrogen

Characterization of the first ever laboratory produced metallic hydrogen sample relies on measurements of optical spectra. Here we present first-principles calculations of the reflectivity of hydrogen between 400 and 600 GPa in the $\mathrm{I4_1/amd}$ 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 to extend the existing optical measurements to the infrared and ultraviolet regions.