Design Topological Materials by Reinforcement Fine-Tuned Generative Model

Abstract

Topological insulators (TIs) and topological crystalline insulators (TCIs) are materials with unconventional electronic properties, making their discovery highly valuable for practical applications. 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$_2$Bi$_2$O$_6$ serving as a representative example--a TI with a full band gap of 0.26 eV, ranking among the largest known in this category.

Figures (4)

• Figure 1: Comparison of SFT and ReFT, and the TIs with large band gaps generated by the fine-tuned generative model.a-b, Comparison between SFT and ReFT in natural language tasks and materials generation tasks, respectively. c-d, Crystal structures, first Brillouin zone and high-symmetry points of the materials X$_{2}$Bi$_{2}$O$_{6}$, where $\text{X}=\text{Ge}, \text{Sn}$. e, Comparison of the band gaps with that of the best-known strong TIs. Data for other materials are taken from Refs. wanglinlin2011zhangjianmin2013. f-g, Band structure with spin-orbit coupling and surface states of Ge$_{2}$Bi$_{2}$O$_{6}$. h-i, Band structure with spin-orbit coupling and surface states of Sn$_{2}$Bi$_{2}$O$_{6}$.
• Figure 2: Illustration of the generative model and the ReFT process.a, Schematic of the overall generation pipeline. The final reward obtained from XBERT is used to update the parameters of the generative model. b, Illustration of the denoising process from $\mathcal{M}_{t}$ to $\mathcal{M}_{t-1}$. In addition to generating (k$_{t-1}$,F$_{t-1}$,A$_{t-1}$) at each step, the model also return the transition probabilities from $\mathcal{M}_{t}$ to $\mathcal{M}_{t-1}$.
• Figure 3: Comparison between the baseline model DiffCSP++ and the fine-tuned model DC+XB.a–c, Changes in validity, novelty, and uniqueness as a function of the number of generated material samples. d–e, Proportion of materials in three categories across all 1,280 generated materials. Results for DiffCSP++ and DC+XB are shown in d and e, respectively. f, Variation in the proportion of generated TIs and TCIs as the number of samples increases.
• Figure 4: Five representative TIs and TCIs exhibiting simple and clean band struture near the Fermi level.a–j, Band structures and crystal structures of the selected materials including CdSb$_{6}$(a-b), Ge$_{2}$Hf$_{2}$(c-d), WAs$_{}$(e-f), SrSn$_{2}$(g-h), and Mo$_{2}$O$_{2}$(i-j). k-l, Edge states and Wannier charge centers of Mo$_{2}$O$_{2}$.