Auxetic Black Phosphorus: A 2D Material with Negative Poisson's Ratio.

The Poisson's ratio of a material characterizes its response to uniaxial strain. Materials normally possess a positive Poisson's ratio - they contract laterally when stretched, and expand laterally when compressed. A negative Poisson's ratio is theoretically permissible but has not, with few exceptions of man-made bulk structures, been experimentally observed in any natural materials. Here, we show that the negative Poisson's ratio exists in the low-dimensional natural material black phosphorus and that our experimental observations are consistent with first-principles simulations. Through applying uniaxial strain along armchair direction, we have succeeded in demonstrating a cross-plane interlayer negative Poisson's ratio on black phosphorus for the first time. Meanwhile, our results support the existence of a cross-plane intralayer negative Poisson's ratio in the constituent phosphorene layers under uniaxial deformation along the zigzag axis, which is in line with a previous theoretical prediction. The phenomenon originates from the puckered structure of its in-plane lattice, together with coupled hinge-like bonding configurations.