Rare-earth polyhydrides formed under pressure are promising conventional superconductors, with the critical temperature $T_c$ in compressed ${\mathrm{LaH}}_{10}$ almost reaching room temperature. Here, we report a systematic computational investigation of the structural and superconducting properties of rare-earth (RE) polyhydrides formed under pressure across the whole lanthanide series. Analyses of the electronic and dynamical properties and electron-phonon coupling interaction for the most hydrogen-rich hydrides ${\mathrm{REH}}_n$ ($n=8,9,10$) that can be stabilized below 400 GPa show that enhanced $T_c$ correlates with a high density of H $s$ states and low number of RE $f$ states at the Fermi level. In addition to previously predicted and measured ${\mathrm{LaH}}_{10}$ and ${\mathrm{CeH}}_9$, we suggest ${\mathrm{YbH}}_{10}$ and ${\mathrm{LuH}}_8$ as additional potential high-$T_c$ superconducters. They form a “second island” of high-$T_c$ superconductivity amongst the late lanthanide polyhydrides, with an estimated $T_c$ of 102 K for ${\mathrm{YbH}}_{10}$ at 250 GPa.

Density functional theory calculations and crystal structure predictions using the particle swarm optimization method have been combined to determine stable hydrides of lead under pressure. In contrast to other group-IVa hydrides, the stoichiometry ${\mathrm{PbH}}_6$ is the first hydride to become stable, at just under 1 Mbar. For two previously studied stoichiometries, ${\mathrm{PbH}}_4$ and ${\mathrm{PbH}}_8$, energetically more favorable phases were identified to become stable around 2 Mbar. In all structures, the hydrogenic sublattices comprise negatively charged ${{\mathrm{H}}_2}^{\delta -}$ molecules. Competitive ${\mathrm{PbH}}_4$ and ${\mathrm{PbH}}_6$ structures are layered. ${\mathrm{PbH}}_6$ features ${\mathrm{H}}_2$ molecules intercalated between hcp Pb layers, the stable phase of dense pure lead, thus offering a potentially straightforward route towards synthesis. In ${\mathrm{PbH}}_8$, the Pb lattice adapts a $\beta$-Sn structure, and hydrogen atoms form quasi-one-dimensional-chains. All structures were found to be metallic and to feature superconductivity in their respective stability range, with moderately high $T_c$ in the range 60–100 K for ${\mathrm{PbH}}_4$ and ${\mathrm{PbH}}_6$ and 161–178 K for ${\mathrm{PbH}}_8$.

Most of the H-rich superconductors have so far been discovered to be clathrate structures. Several clathrate hydrides, including ${\mathrm{H}}_3\mathrm{S}$, ${\mathrm{LaH}}_{10}$, and ${\mathrm{CaH}}_6$, were predicted to be excellent superconductors through structural searches and were later confirmed through experimental synthesis. Here, we conduct extensive crystal structure searches and first-principles calculations for ternary Na-P-H hydrides under high pressure. Two stoichiometries of ${\mathrm{NaPH}}_6$ and ${\mathrm{NaPH}}_8$ in ternary Na-P-H hydrides are found to be stable under 200 GPa. The $P\overline{6}m2$ phase of the ${\mathrm{NaPH}}_6$ hydride is identified as a novel ternary layered H-rich superconductor, exhibiting a high critical temperature $T_c$ of 112.2 K under 200 GPa. Our calculations indicate that the high $T_c$ of the ${\mathrm{NaPH}}_6$ hydride under high pressure is attributed to the high density of hydrogen $s$ states present at the Fermi level. Furthermore, a metastable $Pm\overline{3}$ phase of the clathrate ${\mathrm{NaPH}}_6$ hydride is uncovered under 350 GPa and displays an exceptional $T_c$ of 201.4 K. These results suggest that ternary alkali metal Na-based hydrides hold promise as high-$T_c$ superconductors under high pressure and offer critical insights into the design and synthesis of novel category high-temperature superconductors.