T_c Enhancement Induced by Quantum Ionic Vibrations in Compressed Stannane of P6₃/mmc Phase

High-pressure hydrides have emerged as promising superconducting materials, attracting considerable attention in recent years. In this work, by combining the stochastic self-consistent harmonic approximation with first-principles calculations, we elucidate crucial corrections to the vibrational and superconducting properties arising from quantum and anharmonic ionic vibrations of SnH₄ in P6₃/mmc phase at 150-240 GPa. Compared with the classical harmonic approximation, inclusion of these effects results in a pronounced softening (over 500 cm^-1) of hydrogen-derived optical phonon modes, and increases the superconducting critical temperature (T_c) from 65 K to 79 K (μ^* = 0.1; isotropic Migdal-Eliashberg theory), corresponding to a 22% enhancement. For μ^* = 0.13, the predicted T_c is approximately 70 K. Analysis of the Eliashberg spectral function confirms that hydrogen vibrational modes constitute the dominant tuning mechanism. These results provide quantitative insights into quantum ionic effects in hydride superconductors.