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 temp...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 functionα^(2)F(ω).Here we show that modern machine-learning techniques can substantially improve these formulae,accounting for more general shapes of theα^(2)F function.Using symbolic regression and the SISSO framework,together with a database of artificially generatedα^(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 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.展开更多
基金The work presented here was performed under the auspice of Basic Energy Sciences,United States Department of Energy,contract number DE-SC0020385.
文摘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 functionα^(2)F(ω).Here we show that modern machine-learning techniques can substantially improve these formulae,accounting for more general shapes of theα^(2)F function.Using symbolic regression and the SISSO framework,together with a database of artificially generatedα^(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 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.
