Towards the discovery of high critical magnetic field superconductors

TL;DR

This paper introduces a comprehensive computational database of critical magnetic fields for superconductors, combining advanced theoretical models to identify new high-field materials and challenging existing classifications.

Contribution

It develops a unified computational framework integrating spectral functions, Fermi surfaces, and Eliashberg theory to predict critical magnetic fields across diverse superconductors.

Findings

Large number of Type-I superconductors identified

Higher critical fields associated with larger unit cells

Strong-coupling effects are essential for accurate predictions

Abstract

Superconducting materials are of significant technological relevance for a broad range of applications, and intense research efforts aim at enhancing the critical temperature $T_{c}$. Intriguingly, while numerous studies have explored different computational and machine-learning routes 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 $H_{c}$, $H_{c1}$, and $H_{c2}$ for over 7300 electron-phonon-paired superconductors covering distinct materials classes. A theoretical framework is developed that combines $\alpha^2F(\omega)$ spectral functions and highly accurate Fermi surfaces from density functional theory with clean-limit Eliashberg theory to obtain the 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. We identify the importance of going beyond BCS theory by including strong-coupling corrections to the superconducting gap and electron-phonon renormalizations of the effective mass for predictions of critical fields across materials. These results provide a framework for foundational AI models that realize the concept of inverse materials design for high-$T_{c}$ and high-critical-field superconductors.