Phonon-mediated superconductivity in $${\text{Mg}}_{{1 - x}} {\text{Mo}}_{x} {\text{B}}_{2}$$ Mg 1 - x Mo x B 2 compounds: a crystal prediction via cluster expansion and particle-swarm optimization

Abstract Investigating superconductivity represents one of the most significant phenomena in the field of condensed matter physics. Our simulations aim to elucidate the structures in the metallic state of Mg1−xMoxB2, which is essential for predicting their superconducting properties. By employing a first-principle cluster expansion and particle-swarm optimization, we have predicted the structures of Mg1−xMoxB2 ternary alloys, including Mg0.667Mo0.333B2, Mg0.5Mo0.5B2, and Mg0.333Mo0.667B2, and have determined their thermodynamically stable configurations under both atmospheric and high-pressure conditions. To investigate the potential for superconductivity in these structures, we have conducted a detailed examination of electronic properties that are pertinent to determining the superconducting state. Regarding superconducting properties, Mg0.333Mo0.667B2 exhibits superconductivity with a critical temperature (Tc) of 7.4 K at ambient pressure. These findings suggest that the theoretically predicted structures in Mg/Mo-substituted metal borides could play a significant role in synthesis and offer valuable insights into superconducting materials.