An ab Initio Answer to Long-Debated Questions about Superconducting Nb 3 Sn

Nb 3 Sn is the workhorse superconductor for high-field applications; however, several fundamental aspects remain open 70 years after its discovery. Using anharmonic 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 H c 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 T c and H c 2 , while Nb -site substitution raises H c 2 at the cost of lowering T c .