Data-driven description and prediction of two-dimensional materials with negative Poisson’s ratios

Auxetic materials, which exhibit a negative Poisson’s ratio (NPR), are highly sought for applications ranging from bio-sensors to protective equipment.In contrast to macroscale NPR materials relying primarily on geometric design, the mechanism of NPR in two-dimensional (2D) materials remains poorly understood due to the entangled electronic and lattice degrees of freedom at the atomic scale. Therefore, 2D NPR materials are still relatively rare. In this paper, we present a computational protocol to comprehensively screen 2D NPR materials from 15,632 candidates, discovering 199 new 2D NPR materials. Using 2D transition metal dihalides (MX₂) as a model system, we demonstrate that the NPR emerges from a delicate competition between bond M−X and bond-angle X-M−X stiffnesses, mediated by a synergy of X atom radius and M−X orbital hybridization. Critically, through nonlinear sensitivity analysis and an interpretable machine learning model on 3048 materials with 76 features, we distill this complex physics into two governing descriptors. Finally, we train a deep graph neural network model that accurately predicts the Poisson’s ratios (mean absolute error: 0.045) and Young’s moduli (mean absolute error: 6.7 N/m) of all 2D materials. This work not only elucidates the complex dependence of the NPR effect on intrinsic properties of 2D materials but also establishesa data-driven framework for discovering rare functionalities in 2D systems.