NbTi: A nontrivial puzzle for the conventional theory of superconductivity

We present a comprehensive ab initio study of superconductivity in NbTi, the workhorse for many applications. Despite being a ``textbook'' material, NbTi turns out to be a major challenge for computational superconductivity. In fact, anharmonic effects are crucial to obtain dynamically stable phonons for the ordered bcc phase, unstable at the harmonic level, and beyond-Morel-Anderson effects in the Coulomb interaction reduce the ${T}_{c}$ by more than 20%. Lattice disorder causes an additional large discrepancy in ${T}_{c}$ compared to experiment. Our results imply that a quantitative description of technologically relevant superconductors requires methodological developments beyond the current standards.