An empirical description for the hinge-like mechanism in single-layer black phosphorus: The angle-angle cross interaction

The single-layer black phosphorus is characterized by its puckered configuration that possesses the hinge-like behavior, which leads to the highly anisotropic in-plane Poisson's ratios and the negative out-of-plane Poisson's ratio. We demonstrate that the hinge-like mechanism can be described by the angle-angle cross interaction, which, combined with the bond stretching and angle bending interactions, is able to provide a good description for the mechanical properties of single-layer black phosphorus. We also propose a nonlinear angle-angle cross interaction, which follows the form of Stillinger-Weber potential and can be advantageous for molecular dynamics simulations of single-layer black phosphorus under large deformation.