High-pressure phase stability and superconductivity in La-Zr-H hydrides

Abstract

Hydrogen-rich ternary hydrides are promising candidates for high-Tc superconductivity at megabar pressures, yet their chemical space is vast and largely unexplored. Combining evolutionary structure searches with first-principles calculations, we comprehensively investigate the La-Zr-H ternary system in the 150-300 GPa pressure range. Zero-point energy-corrected convex hull analysis identifies multiple stable superconducting phases, including R3m-Zr2H17 at 300 GPa and P6/mmm-LaZr2H24 at 200 GPa, both of which are thermodynamically and dynamically stable and exhibit strong electron-phonon coupling. Solution of the Eliashberg equations predicts high superconducting transition temperatures of Tc = 209 K for R3m-Zr2H17 at 300 GPa and Tc = 202 K for P6/mmm-LaZr2H24 at 200 GPa. In addition to these stable phases, we identify a high-symmetry metastable compound, P6m2-LaZrH18, which lies just 0.027 eV/atom above the convex hull yet remains dynamically stable and exhibits a high predicted Tc of 206 K at 300 GPa. We find that, across all phases, the elevated Tc correlates with the high-symmetry structure with dense hydrogen cages, favorable electron counts per hydrogen, and a large hydrogen-derived density of states at the Fermi level. Finally, a random- forest machine learning model, trained on diverse hydrides superconductivity data, reproduces these structure-property trends across predicted structures, enabling to identify potential hydrides with high predicted Tc for targeted follow-up calculations and future high-pressure experiments.

Figures (5)

• Figure 1: The ZPE-corrected convex hulls and phase diagrams for the La-Zr-H system ata. 150 GPa b. 200 GPa c. 250 GPa and d. 300 GPa. Black diamonds represent thermodynamically stable phases, while blue circles denote metastable structures with formation enthalpies within 30 meV/atom above the convex hull.
• Figure 2: Crystal structures.a. $R3m$-Zr$_{2}$H$_{17}$. b. $P\bar{6}m2$-LaZrH$_{18}$. c. $P6/mmm$-LaZr$_{2}$H$_{24}$. d. $I4/mmm$-La$_{2}$ZrH$_{12}$. e. Zr-H$_{25}$ and Zr-H$_{27}$ cage in $R3m$-Zr$_{2}$H$_{17}$. f. La-H$_{29}$ and Zr-H$_{29}$ cages in $P\bar{6}m2$-LaZrH$_{18}$. g. La-H$_{30}$ and Zr-H$_{24}$ cages in $P6/mmm$-LaZr$_{2}$H$_{24}$. h. La-H$_{18}$ and Zr-H$_{18}$ cages in $I4/mmm$-La$_{2}$ZrH$_{12}$. Red, blue, and golden yellow spheres represent La, Zr, and H atoms, respectively.
• Figure 3: Phonon dispersion relationships and partial phonon DOSs.a. $R3m$-Zr$_{2}$H$_{17}$ at 300 GPa. b. $P\bar{6}m2$-LaZrH$_{18}$ at 300 GPa. c. $P6/mmm$-LaZr$_{2}$H$_{24}$ at 200 GPa. d. $I4/mmm$-La$_{2}$ZrH$_{12}$ at 250 GPa.
• Figure 4: Electronic band structures and DOSs.a. $R3m$-Zr$_{2}$H$_{17}$ at 300 GPa. b. $P\bar{6}m2$-LaZrH$_{18}$ at 300 GPa. c. $P6/mmm$-LaZr$_{2}$H$_{24}$ at 200 GPa. d. $I4/mmm$-La$_{2}$ZrH$_{12}$ at 250 GPa.
• Figure 5: Eliashberg spectral function ($\alpha^2F$), EPC parameter ($\lambda$), logarithmic average phonon frequency ($\omega_{\log}$), and estimated critical transition temperature ($T_c$).a. $R3m$-Zr$_{2}$H$_{17}$ at 300 GPa. b. $P\bar{6}m2$-LaZrH$_{18}$ at 300 GPa. c. $P6/mmm$-LaZr$_{2}$H$_{24}$ at 200 GPa. d. $I4/mmm$-La$_{2}$ZrH$_{12}$ at 250 GPa.