Coexistence of superconductivity and charge density wave instability in A15-Nb₃Sn

A15-type compound Nb₃Sn has attracted much attention due to its relatively high critical temperature and critical field of superconductivity, making it a leading material for superconducting applications. In this study, we investigate the structural instability and superconductivity of Nb₃Sn under hydrostatic pressure using first-principles calculations. We determine the electronic properties, phonon dispersion, electron-phonon coupling and the superconducting gap for Nb₃Sn at pressures ranging from ambient to 9 GPa. Our results show that a significant electron density is present near the Fermi level due to the van Hove singularity, indicating the strong electron-phonon coupling. The phonon dispersion of Nb₃Sn exhibits Kohn anomalies at three different wave vectors at a lower temperature. Moreover, above a pressure of 6 GPa, the charge density wave (CDW) instability disappeared, suggesting that pressure inhibits the CDW phase. The superconducting temperature is predicted to be T_C = 18.62 K under ambient conditions, which is well consistent with the experimental results. We find that both the CDW and superconducting orders respond to pressure, with their transition temperatures decreasing as the pressure increases below 6 GPa. Above 6 GPa, the superconducting transition temperature increases slowly with pressure. Our results suggest that the instability in Nb₃Sn is driven by the softening of the phonon modes due to the CDW caused by strong electron-phonon coupling. Therefore, the CDW phase and superconducting phase of Nb₃Sn coexist at low pressure.