Electron and phonon band structures of palladium and palladium hydride: A review

Palladium hydride was discovered more than 150 years ago and remains one of the most-studied interstitial metal hydrides because of the richness of its physical behaviours, which include ordered phases and anomalous properties at temperatures below 100 K, a superabundant-vacancy (SAV) phase with stoichiometry Pd₃H₄ formed at high temperature and pressure, and quenching of the enhanced Pauli paramagnetism of palladium. One of the most fascinating properties of palladium hydride is superconductivity at about 10 K without external pressure, in contrast to the newly-discovered polyhydride room-temperature superconductors that require megabar pressures. Moreover, the superconductivity exhibits an inverse isotope effect. Remarkably, modern first-principles approaches are unable to accurately predict the superconducting transition temperature by calculating the electron–phonon coupling constant within Migdal-Eliashberg theory. Anharmonicity of the hydrogen site potential is a key factor and poses a great challenge, since most theoretical approaches are based on the harmonic approximation. This review focuses on the electron and phonon band structures that underpin all such calculations, with palladium as a reference point. While the electron band structures of palladium and its monohydride are uncontroversial, the phonon band structure of palladium hydride in particular is problematic, with a realistic treatment of anharmonicity required – and largely yet to be achieved – to reproduce the results of inelastic neutron scattering experiments. In addition to the monohydride and SAV phases, possible higher hydrides are surveyed and the origin of the famous “50-K” anomaly in specific heat and other physical properties is critically reviewed.