Design Topological Materials by Reinforcement Fine-Tuned Generative Model

However, such materials, particularly those with a full band gap, remain scarce. Given the limitations of traditional approaches that scan known materials for candidates, we focus on the generation of new topological materials through a generative model. Specifically, we apply reinforcement fine-tuning (ReFT) to a pre-trained generative model, thereby aligning the model's objectives with our material design goals. We demonstrate that ReFT is effective in enhancing the model's ability to generate TIs and TCIs, with minimal compromise on the stability of the generated materials. Using the fine-tuned model, we successfully identify a large number of new topological materials, with Ge 2Bi 2O 6 serving as a representative example--a TI with a full band gap of 0.26 eV, ranking among the largest known in this category. Topological materials, including topological insulators (TIs), topological crystalline insulators (TCIs), and topological semimetals (TSMs), represent a fascinating and expansive class of materials whose electronic properties are fundamentally governed by the topology of their electronic bands [1-16]. In particular, TIs [6] and TCIs [8] that feature a full energy gap at the Fermi energy exhibit insulating bulk states and distinct surface or edge states, which are robust against perturbations such as impurities, defects, and disorder. These materials thus hold substantial promise for next-generation technologies, including quantum computing, spintronics, and energy-efficient electronics [2]. Despite over a decade of intensive research on TIs and TCIs, and the discovery of several material systems exhibiting these phases, the number of TIs and TCIs--particularly those with a full bulk gap--remains markedly limited. Consequently, the discovery and identification of real-world materials exhibiting these topological properties continue to represent a critical and ongoing challenge within the field.