Emergence of superconductivity in phase VI of solid hydrogen at high pressures*

Multiple recent experiments claim to observe the transition from insulating to the metallic phase of hydrogen with increasing pressure. However, none of them detected superconductivity even under cryogenic conditions. Contradictory to this, several theoretical investigations showed that superconductivity should exist in already experimentally obtainable pressures. Here we reinvestigate the superconducting properties of solid hydrogen for a recently proposed phase diagram. We show that superconductivity emerges in the Cmca-12 molecular phase VI at pressures at least higher than 450 GPa, an estimate that is shifted to 512 GPa considering more advanced electronic interactions. Our calculations show that quantum anharmonic effects impose a large renormalization of the structure of both molecular and atomic phases, and yield extremely anomalous phonon spectral functions. For the first time ever, we calculate the superconducting critical temperature emph{ab initio} considering the full lineshape of the spectral function and show that it has a non-negligible impact on it.