δ-Phosphorene: a two dimensional material with a highly negative Poisson's ratio

As a basic mechanical parameter, Poisson's ratio (ν) measures the mechanical responses of solids against external loads. In rare cases, materials have a negative Poisson's ratio (NPR), and present an interesting auxetic effect. That is, when a material is stretched in one direction, it will expand in the perpendicular direction. To design modern nanoscale electromechanical devices with special functions, two dimensional (2D) auxetic materials are highly desirable. In this work, based on first principles calculations, we rediscover the previously proposed δ-phosphorene (δ-P) nanosheets [Jie Guan, et al., Phys. Rev. Lett., 2014, 113, 046804] which are good auxetic materials with a high NPR. The results show that the Young's modulus and Poisson's ratio of δ-P are all anisotropic. The NPR value along the grooved direction is up to -0.267, which is much higher than the recently reported 2D auxetic materials. The auxetic effect of δ-P originating from its puckered structure is robust and insensitive to the number of layers due to weak interlayer interactions. Moreover, δ-P possesses good flexibility because of its relatively small Young's modulus and high critical crack strain. If δ-P can be synthesized, these extraordinary properties would endow it with great potential in designing low dimensional electromechanical devices.