A recent experiment reported that robust superconductivity appears in NbTi alloys under ultrahigh pressures with an almost constant superconducting $T_c$ of ~19 K from 120 to 261.7 GPa [J. Guo et al., Adv. Mater. 31, 1807240 (2019)], which is very rare among the known superconductors. We investigate the origin of this novel superconducting behavior in NbTi alloys based on density functional theory and density functional perturbation theory calculations. Our results indicate that the pressure tends to transform NbTi alloys from a random phase to a uniformly ordered crystal phase, and the exotic robust superconductivity of NbTi alloys can still be understood in the framework of BCS theory. The Nb element in NbTi alloys plays a dominant role in the superconductivity at low pressure, while the NbTi crystal with an alternative and uniform Nb and Ti atomic arrangement may be responsible for the stable superconductivity under high pressures. The robust superconducting transition temperature of NbTi under ultrahigh pressure can be explained by a synergistic effect of the enhanced phonon frequency, the modestly reduced total electron-phonon coupling, and the pressure-dependent screened Coulomb repulsion.
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