{"id":"doi:10.1038/s41524-021-00666-7","kind":"article","title":"Machine learning of superconducting critical temperature from Eliashberg theory","authors":["Stephen Xie","Yundi Quan","Ajinkya C. Hire","B. Deng","Jonathan M. DeStefano","I. Salinas","U. S. Shah","Laura Fanfarillo","Jinhyuk Lim","J. Kim","Gregory R. Stewart","J. J. Hamlin","P. J. Hirschfeld","Richard G. Hennig"],"author_count":14,"year":2022,"published":"2022-01-25","venue":"npj Computational Materials","cited_by":86,"doi":"10.1038/s41524-021-00666-7","arxiv_id":null,"nct_id":null,"source_url":"https://doi.org/10.1038/s41524-021-00666-7","archive_url":"https://space-kitty.com/papers/doi:10.1038/s41524-021-00666-7","updated":null,"pmid":null,"pmcid":null,"openalex_id":"W3167076346","pdf_url":"https://www.nature.com/articles/s41524-021-00666-7.pdf","abstract":"Abstract The Eliashberg theory of superconductivity accounts for the fundamental physics of conventional superconductors, including the retardation of the interaction and the Coulomb pseudopotential, to predict the critical temperature T c . McMillan, Allen, and Dynes derived approximate closed-form expressions for the critical temperature within this theory, which depends on the electron–phonon spectral function α 2 F ( ω ). Here we show that modern machine-learning techniques can substantially improve these formulae, accounting for more general shapes of the α 2 F function. Using symbolic regression and the SISSO framework, together with a database of artificially generated α 2 F functions and numerical solutions of the Eliashberg equations, we derive a formula for T c that performs as well as Allen–Dynes for low- T c superconductors and substantially better for higher- T c ones. This corrects the systematic underestimation of T c while reproducing the physical constraints originally outlined by Allen and Dynes. This equation should replace the Allen–Dynes formula for the prediction of higher-temperature superconductors.","abstract_license":"CC-BY (publisher license, via OpenAlex)","license":"cc-by","is_open_access":true,"retracted":false,"peer_reviewed":null,"categories":["Machine Learning in Materials Science"],"details":null,"provenance":"openalex","attribution":"Abstract of \"Machine learning of superconducting critical temperature from Eliashberg theory\" by Stephen Xie, Yundi Quan, Ajinkya C. Hire et al., https://doi.org/10.1038/s41524-021-00666-7, used under its Creative Commons Attribution license (CC-BY); markup removed, otherwise unmodified.","topics":[{"slug":"superconductor-discovery","name":"Computational & AI-Driven Superconductor Discovery","domain_slug":"superconductivity"}],"cited_in_dossiers":[{"slug":"superconductor-discovery","title":"Computational & AI-Driven Superconductor Discovery: State of the Field (October 2026)","url":"https://space-kitty.com/dossiers/superconductor-discovery"}]}