Electron-affinity difference distributions as an organizing principle for superconductivity, enabling the discovery of PtPb$_3$Bi

Abstract

Predicting the superconducting transition temperature ($T_c$) from crystal structure and composition remains a central challenge in condensed-matter physics, reflecting the absence of a broadly predictive framework connecting microscopic bonding to macroscopic quantum behavior. Here, we introduce $\mathcal{GP}$-$T_c$, an interpretable, structure- and chemistry-aware Gaussian process model that enables uncertainty-quantified $T_c$ prediction from experimentally accessible inputs. By encoding local bonding environments as graphlet histograms, we find that the predictive space collapses to a compact set of descriptors: the distribution of electron-affinity (EA) differences between neighboring atoms, together with interatomic distances and simple elemental features, suffices to predict $T_c$ across disparate superconducting families---identifying an overlooked chemical control parameter that underscores the essential role of local structure beyond composition-only approaches. Our results demonstrate that the EA differences serves as an accessible window into electronic structure providing a mechanism-agnostic physical basis that captures $T_c$ across conventional and unconventional families, including doped charge transfer insulators. $\mathcal{GP}$-$T_c$ reproduces the experimentally reported $T_c$ range of the infinite-layer nickelate Nd$_{0.8}$Sr$_{0.2}$NiO$_2$, and we predict and experimentally confirm superconductivity in stoichiometric PtPb$_3$Bi ($T_c \approx 3$~K). To facilitate broad community use, $\mathcal{GP}$-$T_c$ is made available through a web interface for crystal-structure-based prediction, and the same framework identifies additional high-priority superconducting candidates---including SrNiO$_2$ and K(PRh)$_2$---that provide concrete targets for ongoing and future experimental exploration.