  As the simplest element in nature, unraveling the phase diagram of hydrogen
is a primary task for condensed matter physics. As conjectured many decades
ago, in the low-temperature and high-pressure part of the phase diagram, solid
hydrogen is expected to become metallic with a high superconducting transition
temperature. The metallization may occur via band gap closure in the molecular
solid or via a transition to the atomic solid. Recently, a few experimental
studies pushed the achievable pressures into the 400 - 500 GPa range. There are
strong indications that at some pressure in this range metallization via either
of these mechanisms occurs, although there are disagreements between
experimental reports. Furthermore, there are multiple good candidate crystal
phases that have emerged from recent computational and experimental studies
which may be realized in upcoming experiments. Therefore, it is crucial to
determine the superconducting properties of these candidate phases. In a recent
study, we reported the superconducting properties of the C2/c-24 phase, which
we believe to be a strong candidate for metallization via band gap closure [M.
Dogan et al., arXiv:2107.03889 (2021)]. Here, we report the superconducting
properties of the Cmca-12, Cmca-4 and I41/amd-2 phases including the anharmonic
effects using a Wannier function-based dense k-point and q-point sampling. We
find that the Cmca-12 phase has a superconducting transition temperature that
rises from 86 K at 400 GPa to 212 K at 500 GPa, whereas the Cmca-4 and
I41/amd-2 phases show a less pressure-dependent behavior with their Tc in the
74 - 94 K and 307 - 343 K ranges, respectively. These properties can be used to
distinguish between crystal phases in future experiments. Understanding
superconductivity in pure hydrogen is also important in the study of high-Tc
hydrides.
