Unveiling the Mechanism of Negative Poisson’s Ratio in Phosphorus-like 2D MX Materials Driven by Geometric and Electronic Structures

Two-dimensional black-phosphorus-like materials with a re-entrant structure have been reported exhibiting positive or negative Poisson’s ratio (NPR). However, uncovering the underlying geometric–electronic interplay and identifying design principles for NPR materials remain challenging. Using first-principles calculations, we investigate 26 two-dimensional black-phosphorus-like MX monolayers with 10 valence electrons (M = cation, X = anion). Among them, PN, AsN, SbN, AsP, and GeSe exhibit out-of-plane NPR. Geometric structure analysis using machine learning links NPR to the variation of the X–M–X bond angle (θ_M) and M–X–X–X dihedral angle (φ). Under zigzag (y)-direction strain, a larger reduction in θ_M and a greater increase in φ are more favorable for NPR formation. Electronic structure analysis attributes the out-of-plane NPR under y-axis strain to the cation–anion p_z orbital interaction. For NPR materials with the same X element, a higher atomic number of M corresponds to a more negative Poisson’s ratio. This work advances the development of novel materials with unique mechanical behaviors.