Role of anharmonic correction in superconducting phase of two-dimensional alloy Al _0.75 Si _0.25 B ₂ : insight from <i>ab initio</i> anisotropic Migdal–Eliashberg theory

Exploring emergent phases in monolayer alloy superconductors represents a forefront endeavor in contemporary quantum materials research. Following the successful exploration of AlB₂ in a superconducting state, we provide a significant reference for examining superconductivity in Si-substituted AlB₂ using first-principles predictions. This noteworthy outcome highlights that Al_0.75Si_0.25B₂ is one of the energetically stable configurations within the Al_1-<i>x</i>Si_<i>x</i>B₂ system that exhibits the superconducting state. However, the anharmonic effects on this phase significantly impact its phonon spectra, potentially influencing dynamical stability. In specific cases, the application of the stochastic self-consistent harmonic approximation enables us to capture how thermally induced lattice vibrations impact the equilibrium structure of the material. It is observed that the inclusion of anharmonic corrections brings the predicted superconducting characteristics into closer agreement with those derived from the harmonic model, thereby resolving the issue of imaginary frequencies. As a result, we demonstrate that the Allen-Dynes modified McMillan scheme predicts a critical temperature (<i>T</i>_c) of approximately 15 K. This can be enhanced to 41 K through the utilization of the anisotropic Migdal-Eliashberg theory. Our findings reveal that the role of anharmonicity-arising from minor corrections in the acoustic regime contributed by the high atomic mass-in Al_0.75Si_0.25B₂ theoretically leads to superconductivity, with <i>T</i>_c being consistent with values predicted within the harmonic approximation.