T_c enhancement induced by quantum ionic vibrations in compressed stannane of P6₃/mmc phase

High-pressure hydrides represent promising superconducting materials nowadays, attracting considerable attention. In this work, using stochastic self-consistent harmonic approximation combined with first-principles calculations, we reveal crucial corrections to the vibrational and superconducting properties driven by quantum and anharmonic ionic vibrations of SnH₄ in P6₃/mmc phase at 150-240 GPa. Compared to calculations based on classical harmonic approximation, these effects induce over 500 cm^-1 softening of hydrogen-derived optical phonon modes, and elevates the critical temperature (T_c) from 65 K to 79 K (μ^* = 0.1; isotropic Migdal-Eliashberg theory), amounting to a 22% enhancement. At μ^* = 0.13, the predicted T_c is approximately 70 K . Analysis on Eliashberg spectral function confirms hydrogen vibrational modes as the dominant tuning mechanism. This work provides fundamental data quantifying quantum ionic effects in hydride superconductors.