Machine learning of superconducting critical temperature from Eliashberg theory

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 Tc. McMillan, Allen, and Dynes derived approximate closed-form expressions for the critical temperature within this theory, which depends on the electron–phonon spectral function α2F(ω). Here we show that modern machine-learning techniques can substantially improve these formulae, accounting for more general shapes of the α2F function. Using symbolic regression and the SISSO framework, together with a database of artificially generated α2F functions and numerical solutions of the Eliashberg equations, we derive a formula for Tc that performs as well as Allen–Dynes for low-Tc superconductors and substantially better for higher-Tc ones. This corrects the systematic underestimation of Tc 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.

Designing high-TC superconductors with BCS-inspired screening, density functional theory, and deep-learning

“…Moreover, machine learning has become popular in the search for superconductors. There have been several reports of machine-learning applications for finding superconductors 18,[25][26][27] , but thus far they are mostly based on chemical formulas, and lack detailed atomic structure information that can be critical for superconducting behavior.…”

Upper limit of the transition temperature of superconducting materials

“… 25 , 26 , 27 ML models using different algorithms were trained to predict the existence of superconductivity and the T c of superconductors. 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 Progress has been made in several areas, such as how T c varies with doping, 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 the descriptors indicating superconducting mechanism, 36 , 37 , 38 , 39 structural factors affecting T c , 43 , 44 and candidates of new high- T c superconductors. 46 , 51 So far, ML models predicting T c have yielded good predictive scores.…”

Superconducting Materials: Judge, Jury and Executioner of BCS-electron-phonon Theory

“…"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 " [224] (2022).…”