Machine learning of superconducting critical temperature from Eliashberg theory

Xie, S. R.; Quan, Y.; Hire, A. C.; Deng, B.; DeStefano, J. M.; Salinas, I.; Shah, U. S.; Fanfarillo, L.; Lim, J.; Kim, J.; Stewart, G. R.; Hamlin, J. J.; Hirschfeld, P. J.; Hennig, R. G.

doi:10.1038/s41524-021-00666-7

Machine learning of superconducting critical temperature from Eliashberg theory

Journal Article · Tue Jan 25 00:00:00 EST 2022 · npj Computational Materials

DOI:https://doi.org/10.1038/s41524-021-00666-7· OSTI ID:1842233

Xie, S. R.; Quan, Y.; ; ; ; Salinas, I.; Shah, U. S.; Fanfarillo, L.; ; Kim, J.; Stewart, G. R.; Hamlin, J. J.; Hirschfeld, P. J.;

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.

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Research Organization:: University of Florida, Gainesville, FL (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0020385

OSTI ID:: 1842233

Alternate ID(s):: OSTI ID: 2341713
OSTI ID: 1978595

Journal Information:: npj Computational Materials, Journal Name: npj Computational Materials Journal Issue: 1 Vol. 8; ISSN 2057-3960

Publisher:: Nature Publishing GroupCopyright Statement

Country of Publication:: United Kingdom

Language:: English

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