NbTi: a nontrivial puzzle for the conventional theory of superconductivity

In this paper we present the first ab-initio study of the superconducting state of NbTi, traditionally considered the main workhorse for many large-scale superconducting applications. Despite its apparent simplicity, this compound represents a major challenge for current computational standards in superconductivity. Using the newly developed SSCHA-MLIP framework, we demonstrate that anharmonic effects are required to obtain stable phonon dispersions for the ordered bcc phase, which is unstable at the harmonic level. We also find that treating the residual Coulomb interaction in the newly-developed Kukkonen-Overhauser scheme reduces the T_c by more than 20 % compared to the simple Morel-Anderson approximation. We show that the unusually large residual discrepancy in T_c with respect to experiment should be attributed to lattice disorder, which we treat with a simple model of Boltzmann-averaged supercells. Our results indicate that a quantitative description of technologically-relevant transition metal alloy superconductors requires methodological developments to account for lattice disorder that go beyond the current standards in computational superconductivity.