(color online) (a) Monolayer phosphorene lattice and ten types of intra-layer hoppings. (b) Bilayer phosphorene lattice and five types of inter-layer hoppings. The red- and blue-filled circles denote puckered-up and puckered-down phosphorus atoms, the solid and semitransparent meshes represent the upper and lower phosphoene layer respectively, and the rectangle shows the unit cell.