Phase stability and superconductivity of lead hydrides at high pressure

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 ${\mathrm{PbH}}_8$.

Figure 1

The enthalpies per formula unit and decomposition enthalpies as a function of pressure for (a) ${\mathrm{PbH}}_4$, (b) ${\mathrm{PbH}}_6$, and (c) ${\mathrm{PbH}}_8$. The reported structures for Pb [44], ${\mathrm{H}}_2$ [45], and Pb-H [25, 31] compounds are considered. Phases from the literature are drawn with open symbols and dashed lines; phases from this work are shown by solid symbols and solid lines.

Figure 2

Phase stabilities of lead hydrides. (a) Formation enthalpies of different Pb-H compounds at specific pressures. (b) Predicted ground state pressure-composition phase diagram of lead hydrides.

Figure 3

Crystal structures of high-pressure lead hydrides. (a) $P6mm {\mathrm{PbH}}_4$ at 250 GPa, (b) $Pmmn {\mathrm{PbH}}_4$ at 300 GPa, (c) $C{222}_1{\mathrm{PbH}}_6$ at 100 GPa, and (d) $Fddd {\mathrm{PbH}}_8$ at 200 GPa. Green spheres represent Pb atoms, and yellow, light purple, and dark cyan represent crystallographically distinct H atoms as labeled. Coordination polyhedra of Pb atoms are indicated in each structure.

Figure 4

(a) Charge density topology analysis of $Fddd {\mathrm{PbH}}_8$ with cross sections that show charge density contours (green lines) and gradients (black lines). (b) Calculated phonon dispersion (the radius of the black circle is proportional to the phonon linewidth), projected phonon density of states, Eliashberg phonon spectral function ${\alpha }^{2}F\left(\omega \right)$, and integrated electron-phonon coupling $\lambda \left(\omega \right)$ for $Fddd {\mathrm{PbH}}_8$ at 200 GPa.

Figure 5

The calculated electronic band structure and projected DOS for (a) $P6mm {\mathrm{PbH}}_4$ at 250 GPa, (b) $Pmmn {\mathrm{PbH}}_4$ at 300 GPa, (c) $C{222}_1 {\mathrm{PbH}}_6$ at 100 GPa, and (d) $Fddd {\mathrm{PbH}}_8$ at 200 GPa.

Figure 6

-PCOHP for pairs of Pb-H, H-H, and $\mathrm{H}\cdots \mathrm{H}$ in (a) $P6mm {\mathrm{PbH}}_4$ at 250 GPa, (b) $Pmmn {\mathrm{PbH}}_4$ at 300 GPa, (c) $C{222}_1 {\mathrm{PbH}}_6$ at 100 GPa, and (d) $Fddd {\mathrm{PbH}}_8$ at 200 GPa. Energies are normalized to the respective Fermi level.