Single-layer Ag 2 S: A two-dimensional bi-directional auxetic semiconductor.

Two-dimensional auxetic materials have attracted considerable attention due to their potential applications in medicine, tougher composites, defense and so on. However, they are scare especially at low dimension, as auxetic materials are mainly realized in engineered materials and structures. Here using first-principles calculations, we identify a compelling two-dimensional auxetic material, single-layer Ag2 S, which possesses large negative Poisson's ratios in both in-plane and out-of-plane directions, but anisotropic ultra-low Young's modulus. Such a coexistence of simultaneous negative Poisson's ratios in two directions is extremely rare, which is mainly originated from its particular zigzag-shaped buckling structure. In addition, contrary to the previously known metal-shrouded single-layer M2 X (M = metal, X = nonmetal), single-layer Ag2 S is the first nonmetal-shrouded M2 X. Electronic calculations show that it is an indirect-gap semiconductor with gap value of 2.83 eV, and it can be turned to be direct with strain. These intriguing properties make single-layer Ag2 S a promising auxetic material in electronics and mechanics.