Forward and Inverse design of high $T_C$ superconductors with DFT and deep learning

We developed a multi-step workflow for the discovery of next-generation conventional superconductors. 1) We started with a Bardeen–Cooper–Schrieffer (BCS) inspired pre-screening of 55000 materials in the JARVIS-DFT database resulting in 1736 materials with high Debye temperature and electronic density of states at the Fermi-level. 2) Then, we performed density functional theory (DFT) based electron-phonon coupling calculations for 1058 materials to establish a systematic database of superconducting properties. 3) Further, we applied forward deep-learning (DL) using atomistic line graph neural network (ALIGNN) models to predict properties faster than direct first-principles computations. Notably, we find that by predicting the Eliashberg function as an intermediate quantity, we can improve the model performance versus a direct DL prediction of $T_C$. Finally, 4) we used an inverse deep-learning method with a crystal diffusion variational autoencoder (CDVAE) model to generate thousands of new superconductors with high chemical and structural diversity. 5) We screened these CDVAE-generated structures using ALIGNN to identify candidates that are stable with high $T_C$. 6) We verified the top superconducting candidates with DFT.