Discovery of 2D Materials via Symmetry-Constrained Diffusion Model

Generative models for 2D materials have shown significant promise in accelerating the material discovery process. The stability and performance of these materials are strongly influenced by their underlying symmetry. However, existing generative models for 2D materials often neglect symmetry constraints, leading to a tendency to generate overly complex, low-symmetry structures. Here, we introduce a symmetry-constrained diffusion model (SCDM) that integrates space group symmetry into the generative process. By incorporating Wyckoff positions, the model ensures adherence to symmetry principles, leading to the generation of 2,000 candidate structures. DFT calculations were conducted to evaluate the energy above the convex hull (Ehull) of these structures after structural relaxation. From the generated samples, 843 materials that met the energy stability criteria (Ehull < 0.6 eV/atom) were identified. Among these, six candidates were selected for further stability analysis, including phonon band structure evaluations and electronic property investigations, all of which exhibited phonon spectrum stability. To benchmark the performance of SCDM, a symmetry-unconstrained diffusion model was also evaluated via crystal structure prediction, with detailed comparisons revealing key advantages of symmetry constraints. The results highlight that incorporating symmetry constraints enhances the effectiveness of generated 2D materials, contributing to the discovery of 2D materials through generative modeling.