We present first-principles calculations of metallic atomic hydrogen in the 400-600 GPa pressure range in a tetragonal structure with space group I41/amd, which is predicted to be its first atomic phase. Our calculations show a band structure close to the free-electron-like limit due to the high electronic kinetic energy induced by pressure. Bands are properly described even in the independent electron approximation fully neglecting the electron-electron interaction. Linear-response harmonic calculations show a dynamically stable phonon spectrum with marked Kohn anomalies. Even if the electron-electron interaction has a minor role in the electronic bands, the inclusion of electronic exchange and correlation in the density response is essential to obtain a dynamically stable structure. Anharmonic effects, which are calculated within the stochastic self-consistent harmonic approximation, harden high-energy optical modes and soften transverse acoustic modes up to a 20% in energy. Despite a large impact of anharmonicity has been predicted in several high-pressure hydrides, here the superconducting critical temperature is barely affected by anharmonicity, as it is lowered from its harmonic 318 K value only to 300 K at 500 GPa. We attribute the small impact of anharmonicity on superconductivity to the absence of softened optical modes and the fairly uniform distribution of the electron-phonon coupling among the vibrational modes.
First-principles calculations based on density-functional theory including anharmonicity within the variational stochastic self-consistent harmonic approximation are applied to understand how the quantum character of the proton affects the candidate metallic molecular Cmca - 4 structure of hydrogen in the 400-450 GPa pressure range, where metallization of hydrogen is expected to occur. Anharmonic effects, which become crucial due to the zero-point motion, have a large impact on the hydrogen molecules by increasing the intramolecular distance by approximately a 6%. This induces two new electron pockets at the Fermi surface opening new scattering channels for the electron-phonon interaction. Consequently, the electron-phonon coupling constant and the superconducting critical temperature are approximately doubled by anharmonicity and Cmca - 4 hydrogen becomes a superconductor above 200 K in all the studied pressure range. Contrary to many superconducting hydrides, where anharmoncity tends to lower the superconducting critical temperature, our results show that it can enhance superconductivity in molecular 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 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 extending the optical measurements to the infrared and ultraviolet regions as our results suggest optical measurements can potentially identify high-pressure phases of hydrogen.
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