First-principles search of hot superconductivity in La-X-H ternary hydrides

Motivated by the recent claim of hot superconductivity with critical temperatures up to 550 K in La + x hydrides, we investigate the high-pressure phase diagram of compounds that may have formed in the experiment, using first-principles calculations for evolutionary crystal structure prediction and superconductivity. Starting from the hypothesis that the observed T-c may be realized by successive heating upon a pre-formed LaH10 phase, we examine plausible ternaries of lanthanum, hydrogen and other elements present in the diamond anvil cell: boron, nitrogen, carbon, platinum, gallium, gold. We find that only boron and, to a lesser extent, gallium form metastable superhydride-like structures that can host high-T-c superconductivity, but the predicted T-c's are incompatible with the experimental reports. Our results indicate that, while the claims of hot superconductivity should be reconsidered, it is very likely that unknown H-rich ternary or multinary phases containing lanthanum, hydrogen, and possibly boron or gallium may have formed under the reported experimental conditions, and that these may exhibit superconducting properties comparable, or even superior, to those of currently known hydrides.