High-T_c Superconducting Hydrides Formed by LaH₂₄ and YH₂₄ Cage Structures as Basic Blocks

Based on recent studies regarding high-temperature (high-$T_c$) La-Y ternary hydrides (e.g., $P{\bar{1}}$-La$_2$YH$₁₂$, $Pm{\bar{3}}m$-LaYH$₁₂$, and $Pm{\bar{3}}m$-(La,Y)H$₁₀$ with a maximum $T_c \sim 253$ K), we examined the phase and structural stabilities of the (LaH$_6$)(YH$_6$)$_y$ series as high-$T_c$ ternary hydride compositions using a genetic algorithm and $\it ab$ $\it initio$ calculations. Our evaluation showed that the $Pm\bar{3}m$-LaYH$₁₂$ reported in the previous study was unstable during decomposition into $R\bar{3}c$-LaH$₆$ + $Im\bar{3}m$-YH$₆$. We also discovered new crystal structures, namely $Cmmm$-LaYH$₁₂$ ($y=1$), $R\bar{3}c$-LaYH$₁₂$ ($y=1$), $Cmmm$-LaY$_3$H$₂₄$ ($y=3$), and $R\bar{3}$-LaY$_3$H$₂₄$ ($y=3$), showing stability against such decomposition. While $R\bar{3}c$ ($y=1$) and $R\bar{3}$ ($y=3$) did not exhibit superconductivity owing to the extremely low density of states at the Fermi level, $Cmmm$ phases exhibited a $T_c$ of approximately 140~K at around 200~GPa owing to the extremely high electron--phonon coupling constant ($\lambda$ = 1.876 for LaYH$₁₂$). By the twice longer stacking for $Cmmm$-LaY$_3$H$₂₄$, the coupling constant increased owing to the chemical pressure of Y, leading to a slightly increased $T_c$.