Towards the discovery of high critical magnetic field superconductors

Superconducting materials are of significant technological relevance, and intense research efforts aim at enhancing the critical temperature T c . Intriguingly, while numerous computational and machine-learning approaches have been developed to predict T c , the fundamental role of the critical magnetic field has so far been overlooked. Here we open a new frontier in superconductor discovery by presenting a consistent computational database of critical fields H c , H c 1 , and H c 2 for ~7300 electron-phonon-mediated superconductors covering diverse materials classes. Combining α 2 F ( ω ) spectral functions and accurate Fermi surfaces from density functional theory with clean-limit Eliashberg theory, we compute coherence lengths, London penetration depths, and Ginzburg-Landau parameters. We discover an unexpectedly large number of Type-I superconductors and show that larger unit cells generically support higher critical fields and Type-II behavior. Accounting for strong-coupling and mass-renormalization effects beyond BCS theory proves essential for accurate predictions. The results enable AI-guided inverse-design strategies for high- T c and high-critical-field superconductors.