Ab initio prediction of superconductivity in molecular metallic hydrogen under high pressure

We present a first ab initio investigation of the electron–phonon coupling (EPC) of molecular metallic hydrogen with a Cmca structure based on the linear-response approach. This molecular metallic hydrogen with overlapping bands has an elastic instability at lower pressures (<300 GPa), but stabilizes dynamically under further compression as indicated by the absence of phonon softening, thus supporting the choice of Cmca   structure as a good candidate for metallic hydrogen. Within the conventional BCS theory, the predicted critical temperature TcTc is 107 K at 347 GPa, so indicating good candidacy for a high temperature superconductor. With increasing pressure, interestingly, the EPC parameter λλ, hence, TcTc increases, resulting from the increased electronic density of states at the Fermi level and EPC matrix element 〈I2〉〈I2〉, in spite of an enhanced average phonon frequency 〈ω2〉〈ω2〉.