Strong Electron-Phonon and Band Structure Effects in the Optical Properties of Superconducting Hydrogen

Early in this year, Dias and Silvera [Science 355, 715 (2017)] reported the first ever laboratory-produced sample of metallic hydrogen at 495 GPa. As most breakthroughs in science, this claim came along with tremendous controversy, being the pressure calibration and sample characterization the main issues put under question.

Here we present first-principles calculations of the reflectivity of hydrogen between 400 and 600 GPa in the I4₁/amd crystal structure, the one predicted at these pressures. Our calculations combine time-dependent density functional and Eliashberg theories, thus, taking into account both electronic band structure and electron-phonon scattering effects. Our results predict 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 experimental electronic scattering rates in the 0.7-3 eV range are in agreement with our theoretical estimations, showing scattering is dominated by the electron-phonon interaction.

In conclusion, our results shine some light to the already measured frequency range while they strongly encourage the extension of optical experiments to broader regimes.