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.

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Recent studies have predicted that magnetic EuCd 2 As 2 can host several different topological states depending on its magnetic order, including a single pair of Weyl points. Here we report on the bulk properties and band inversion induced by pressure in the nonmagnetic analogs AECd 2 As 2 (AE = Ca, Sr, Ba) as studied with density functional theory calculations. Under ambient pressure we find that these compounds are narrow band gap semiconductors, in agreement with experiment. The size of the band gap is dictated by both the increasing ionicity across the AE series which tends to increase the band gap, as well as the larger nearest neighbor Cd-As distance from increasing atomic size which can decrease the band gap because the conduction band edge is an antibonding state derived mostly from Cd 5s orbitals. The combination of these two competing effects results in a nonmonotonic change of the band gap size across the AE series with SrCd 2 As 2 having the smallest band gap among the three compounds. The application of negative pressure reduces this band gap and causes the band inversion between the Cd 5s and As 4p orbitals along the -A direction to induce a pair of Dirac points. The topological nature of the Dirac points is then confirmed by finding the closed Fermi arcs on the (10 10) surface.

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