An ab initio answer to long-debated questions about superconducting Nb3⁢Sn

Nb3⁢Sn is the workhorse superconductor for high-field applications; however, several fundamental aspects remain open 70 years after its discovery. Using anharmonic ab initio Migdal-Eliashberg theory, we resolve three key questions: (1) the cubic-to-tetragonal martensitic transition is weakly first order; (2) the superconducting gap is strongly anisotropic but continuous over the Fermi surface; and (3) the drop of 𝐻𝑐⁢2 across the transition arises from both reduced electron-phonon coupling and a redistribution of Fermi velocities. The orbital origin of the gap anisotropy suggests targeted doping strategies: Sn-site substitution can increase both 𝑇𝑐 and 𝐻𝑐⁢2, while Nb-site substitution raises 𝐻𝑐⁢2 at the cost of lowering 𝑇𝑐.