Effect of spin-orbit coupling on the superconductivity in the lead hydrides under high pressure

The spin-orbit coupling (SOC) effect of heavy elements has the capacity to influence the electron structure and properties of materials. Previous studies have demonstrated that the SOC effect enhances the electron-phonon coupling constant (EPC \ensuremath{\lambda}) of elemental Pb and Pb-containing compounds in theory. However, the opposite phenomenon is found in the hydrides of lead that we studied, i.e., the SOC effect reduced the EPC \ensuremath{\lambda}. Moreover, previous studies have not clearly elucidated the underlying physical mechanism through which SOC effects impact superconductivity. Furthermore, the effects of SOC in Pb-H compounds under high pressure remain unexplored. Here, we investigated the structures of the Pb-H system and the EPC mechanism under the action of SOC at pressures. A new $P{2}₁/m\text{\ensuremath{-}}\mathrm{Pb}{\mathrm{H}}₂$ hydride has been discovered to be more stable under high pressure than previously reported. The new lead superhydrides have been identified, including Cmcm-$\mathrm{Pb}{\mathrm{H}}₁₀$, which contains a linear ${\mathrm{H}}₄$ macromolecule with double covalent bonds. The superconducting critical temperature (${T}_c$) of lead superhydrides is significantly lower than that of $\mathrm{Y}{\mathrm{H}}₁₀$ and $\mathrm{La}{\mathrm{H}}₁₀$. This is due to the fact that hydrogen exists in the form of a large number of ${\mathrm{H}}₂$ molecules without forming a cagelike supramolecular structure. In Pb, in addition to the previously reported reason of phonon softening, we have identified another important factor contributing to the increase in EPC \ensuremath{\lambda}: the enhancement of the average electron-phonon interaction at the Fermi surface due to the SOC effect. In Pb-H compounds, the SOC effect leads to the topological transformation of the Fermi surface, and increases the probability of charges appearing near H-H bonds and the twisting vibration frequency of hydrogen molecules, which is the important reason for the decline of EPC \ensuremath{\lambda}. In the Pb-H system, the SOC effect can result in an increase in the average phonon frequency and a decrease in EPC \ensuremath{\lambda}. The superconducting ${T}_c$ is dependent upon the competition between the decreased EPC \ensuremath{\lambda} and the increased Debye temperature.