Band-gap tunability and dynamical instability in strained monolayer and bilayer phosphorenes. 
Very recently, field-effect transistors based on few-layer phosphorene crystals with a thickness of down to a few nanometres were successfully fabricated, triggering interest in this new functional two-dimensional material.  In this work, we apply first-principles calculations to studying the evolution of electronic and phononic structures with out-of-plane strain for monolayer and bilayer phosphorenes.  It is found that the vertical stress can be used to tune the band gap of a semiconducting phosphorene in a wide range.  On the other hand, the vertical stress can make the phosphorene lattice become dynamically unstable and surface reconstruction or structural phase transition may occur.  Due to the interlayer van der Waals coupling, the dynamically stable range of bilayer phosphorene under vertical stress is wider than that of monolayer phosphorene.  It is proposed whether or not a semiconductor-semimetal transition occurring in a strained phosphorene is determined not only by its band gap closing, but also by its lattice stability against strain.  This information is essential for the strain engineering of phosphorene and future device fabrication.