Superconductivity of ${\mathrm{LaH}}_{10}$ and ${\mathrm{LaH}}_{16}$ polyhydrides

Recent experiments have established previously predicted ${\mathrm{LaH}}_{10}$ as the highest-temperature superconductor, with $T_C$ up to 250–260 K [Drozdov et al., Nature (London) 569, 528 (2019); Somayazulu et al., Phys. Rev. Lett. 122, 027001 (2019)]. In this work we explore the high-pressure phase stability and superconductivity of lanthanum hydrides ${\mathrm{LaH}}_m$. We predict the stability of the hitherto unreported polyhydride $P6/mmm-{\mathrm{LaH}}_{16}$ at pressures above 150 GPa; at 200 GPa, its predicted superconducting $T_C$ is 156 K, the critical field ${\mu }_0{H}_C\left(0\right)$ is approximately 35 T, and the superconducting gap is up to 35 meV. We revisit the superconductivity of ${\mathrm{LaH}}_{10}$ and find its $T_C$ to be up to 259 K at 170 GPa from solving the Eliashberg equation and 271 K from solving the gap equation within the superconducting density functional theory, which also allows us to compute the Coulomb pseudopotential ${\mu }^{*}$ for ${\mathrm{LaH}}_{10}$ and ${\mathrm{LaH}}_{16}$.

Figure 1

Convex hull diagrams for the La-H system at (a) 50, (b) 100, (c) 150, and (d) 200 GPa. The metastable and stable phases are marked by blue squares and black circles, respectively.

Figure 2

Crystal structures of (a) $C2/m-{\mathrm{LaH}}_{10}$, (b) $R\overline{3}m-{\mathrm{LaH}}_{10}$, (c) $Fm\overline{3}m-{\mathrm{LaH}}_{10}$, and (d) hydrogen ${\mathrm{H}}_{32}$ cage common for these phases; (e) the Eliashberg ${\alpha }^{2}F\left(\omega \right)$ function (black curve), phonon density of states (orange), cumulative ${\omega }_{\log }$ (red), EPC coefficient λ (blue), and critical transition temperature $T_C$ (green) of $Fm\overline{3}m-{\mathrm{LaH}}_{10}$ at 170 GPa. The crystal structures were generated using vesta software [56]; the atoms of La and hydrogen are shown as large orange and small black balls, respectively; blue arrows show displacements of the hydrogen atoms away from their positions in a perfect cubic ${\mathrm{H}}_8$ cluster.

Figure 3

(a) Crystal structure of $P6/mmm-{\mathrm{LaH}}_{16}$ at 150 GPa; (b) band structure and DOS of ${\mathrm{LaH}}_{16}$ (red lines are for La, blue lines are for H) at 250 GPa; (c) the Eliashberg function ${\alpha }^2\mathrm{F}\left(\omega \right)$ (black), cumulative ${\omega }_{\log }$ (red), and the EPC coefficient λ (blue) of $P6/$mmm-${\mathrm{LaH}}_{16}$ at 200 GPa.

Figure 4

Superconducting temperatures $T_C$, obtained using the A-D formula with ${\mu }^{*}=0.1$, and critical magnetic fields for a series of lanthanum hydrides at 150 and 180 GPa.