Einstein, Debye, and Fermi Temperatures, Electron-Phonon Coupling Constant and Parabolic Pressure Dependence of the Transition Temperature in the Y0.5Ce0.5H9 Hydride Superconductor

Abstract

Ternary and quaternary hydride superconductors have been the focus of intensive experimental and first-principles calculations studies in recent years. A primary approach in experimental synthesis of ternary and quaternary hydrides is to substitute La or Ce ions by other rare-earth elements in LaH₁₀ and CeH₉ phases, respectively. The choice of CeH₉ as a matrix phase to synthesise ternary and quaternary hydrides is because this phase exhibits transition temperatures above 70 K at a relatively low-pressure p = 90–130 GPa. One of the synthesized phases by this approach, where cerium is substituted by yttrium, is the ternary P6₃/mmc-Y_0.5Ce_0.5H₉ hydride phase. This phase exhibits the onset of superconducting transition temperature T_c = 100–140 K in the pressure range of p = 98–155 GPa. Here, based on the analysis of reported experimental data by Chen et al. (https://doi.org/10.1038/s41467-024-46133-x), I found that the onset of the superconducting transition temperature in Ce_0.5Y_0.5H₉ obeys the parabolic dependence on pressure, T_c,onset(P)/T_c,onset,max = (1–95*(P-0.145)²), where T_c,max = 140 K, and P is in TPa. The revealed dependence of T_c(P) is remarkably similar to that of T_c(p) in cuprates, where p is the doping state. Furthermore, the evolution of the Einstein and Debye temperatures and the electron-phonon coupling strength with pressure have been derived for the P6₃/mmc-Y_0.5Ce_0.5H₉ phase.