Physics informed inverse discovery of potential topological materials via descriptor-graph ensemble learning

Abstract

Topological materials (TMs) constitute a fundamentally new class of quantum matter, hosting symmetry protected electronic states with robust transport and spin–momentum locking that are central to next generation electronic, spintronic, and quantum technologies. However, their identification is conventionally driven by first principles electronic structure calculations and explicit evaluation of topological invariants, which limits scalability across large chemical spaces. Here, we present a physics informed machine learning (ML) framework for discovering topologically non-trivial materials without repeated evaluation of wavefunction based topological invariants during candidate screening, integrating electronic structure–derived proxy descriptors, symmetry-resolved topological databases, tabular ML models, and crystal graph neural networks (GNNs) into a unified prediction and inverse discovery pipeline. Using symmetry indicator derived Z2 invariants (ν0, ν1, ν2, ν3) as supervised labels, we curate a database of 9,142 crystalline materials spanning multiple dimensionalities and construct a ML dataset comprising 6,436 two- and three-dimensional materials and construct physically motivated descriptors capturing band gaps, bandwidths, Fermi level crossings, and dispersion characteristics alongside composition and structure-based representations. Tabular models achieve ROC–AUC values > 0.8, while GNNs trained solely on atomic connectivity achieve > 0.65, suggesting that crystal structure contains useful but incomplete information related to topological propensity. In an inverse discovery setting, the models assign probabilistic scores and enable consensus ranking that filters approximately 45,000 candidates to about 1,200 candidate materials for subsequent validation. We shortlist 100 top-ranked materials for future validation using first principles electronic structure calculations and topological studies. Overall, this work establishes a scalable and physics guided candidate prioritization framework for inverse discovery of topological materials beyond brute force electronic structure calculations.