Exploration of stable compounds, crystal structures, and superconductivity in the Be-H system

Using first-principles variable-composition evolutionary methodology, we explored the high-pressure structures of beryllium hydrides between 0 and 400 GPa. We found that BeH$_2$ remains the only stable compound in this pressure range. The pressure-induced transformations are predicted as $Ibam$ $\rightarrow $ $P\bar{3}m1$ $\rightarrow $ $R\bar{3}m$ $ \rightarrow $ $Cmcm$ $ \rightarrow $ $P4/nmm$, which occur at 24, 139, 204 and 349 GPa, respectively. $P\bar{3}m1$ and $R\bar{3}m$ structures are layered polytypes based on close packings of H atoms with Be atoms filling octahedral voids in alternating layers. $Cmcm$ and $P4/nmm$ structures have 3D-networks of strong bonds, but also feature rectanular and squre, respectively, layers of H atoms with short H-H distances. $P\bar{3}m1$ and $R\bar{3}m$ are semiconductors while $Cmcm$ and $P4/nmm$ are metallic. We have explored superconductivity of both metallic phases, and found large electron-phonon coupling parameters of $ \lambda $=0.63 for $Cmcm$ (resulting in a $T_c$ of 32.1-44.1 K) at 250 GPa and $ \lambda $=0.65 for $P4/nmm$ ($T_c$ = 46.1-62.4 K) at 400 GPa. The dependence of $T_c$ on pressure indicates that $T_c$ initially increases to a maximum of 45.1 K for $Cmcm$ at 275 GPa and 97.0 K for $P4/nmm$ at 365 GPa, and then decreases with increasing pressure for both phases.