Exploring phonon mediated superconductivity of [Formula: see text] and [Formula: see text] under high pressure insight from first-principles calculations.

Investigating novel materials under high pressure presents a challenge in condensed matter physics. In this study, we examine [Formula: see text] and [Formula: see text], materials identified through an evolutionary algorithm, which exhibit thermodynamic stability up to at least 100 GPa. Our findings reveal that [Formula: see text] exhibits a rhombohedral structure ([Formula: see text]) at pressures ranging from 0 GPa to 25 GPa, transitioning to a hexagonal structure ([Formula: see text]) between 50 GPa and 100 GPa. In contrast, [Formula: see text] is predicted to have a monoclinic structure (C2/m) at low pressures and a hexagonal structure ([Formula: see text]) at higher pressures. Notably, both materials are dynamically stable within the harmonic approximation at pressures beyond 15 GPa for [Formula: see text] and beyond 25 GPa for [Formula: see text]. Furthermore, accurately capturing the thermal lattice vibrations of these materials under strong quantum anharmonicity requires advanced methods. Using a stochastic approach to self-consistent harmonic approximation (SSCHA), we introduce anharmonic corrections to further explore lattice dynamics. For superconducting properties, [Formula: see text] shows a remarkable critical temperature ([Formula: see text]) of 44.5 K at a pressure of 25 GPa, as predicted within the harmonic approximation. In comparison, [Formula: see text] achieves a [Formula: see text] of approximately 13 K at a pressure of 50 GPa when anharmonic corrections are applied using the Allen-Dynes modified McMillan equation. Our findings bridge a gap in understanding electronic band structure, phonon linewidth impacts, and vibrational modes under pressure, offering key insights into phase stability and superconducting mechanisms. These findings introduce a promising new class of materials, emphasizing their potential to enrich superconductivity research by advancing previously overlooked substances.