# Computational & AI-Driven Superconductor Discovery: State of the Field (October 2026)

Research dossier · v1 · updated 2026-10-30 · 3,274 words · 44 sources · 29 claims · verification: verified

Covers ab initio Migdal-Eliashberg calculations, machine-learning models of critical temperature, high-throughput electron-phonon screening and the reported high-pressure hydride record. The main takeaway: first-principles Migdal-Eliashberg calculations reproduce well-studied conventional superconductors such as MgB2, while predictions for new chemistries remain unvalidated until synthesized and independently measured.

## Contents

- Executive summary
- Background and core concepts
- Timeline of key milestones
- State of the art
  - Ab initio Migdal-Eliashberg calculations
  - Machine-learning models of critical temperature
  - High-throughput and surrogate-accelerated screening
  - Hydrides under pressure
  - Quantitative benchmarks
- Open problems and active debates
- Major programs and players
- Outlook: what to watch (next 12-18 months)
- Key papers
- Glossary

## Sample findings

- An anisotropic first-principles Eliashberg calculation reproduced a critical temperature of about 39 K for MgB2 with a coupling constant near 0.61.
- Standard Eliashberg estimates for undoped LaOFeAs gave a coupling constant of about 0.21 and a maximum Tc near 0.8 K; a coupling 5-6 times larger would be needed to reproduce the observed Tc of 26 K.

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