Superconductivity in hexagonal Ce_0.5La_0.5H₉ under high pressure

Recently, experimental observation has shown that the substitutional alloy (Ce,La)H₉ can be successfully synthesized under high pressure, approximately 90-170 GPa, and become a superconductor with a high critical temperature (T_c) superconductivity in ternary rare-earth clathrate hydrides between 148-178 K. In this work, we theoretically simplified the hydride alloy (Ce,La)H₉, a compound in a series that could function as a potential superconductor, with Ce_0.5La_0.5H₉ exhibiting strong electron-phonon coupling (EPC). The Ce_0.5La_0.5H₉ alloy is scrutinized for its lattice dynamical stability in the pressure range of 100 to 150 GPa. Remarkably, we have first unlocked the theoretical structure of Ce_0.5La_0.5H₉, which remains ambiguous in identifying its crystal structure through experimental measurements. With these remarkable results, the Ce_0.5La_0.5H₉ begins to exhibit structural stability at 110 GPa. The superconducting spectral function is also calculated. We found that the EPC reaches strong-coupling at a pressure of 120 GPa. Using the Allen-Dynes-modified McMillan equation in the strong coupling regime, the Ce_0.5La_0.5H₉ exhibits superconductivity with a T_c of approximately 127 K.