The electronic origin of shear-induced direct to indirect gap transition and anisotropy diminution in phosphorene

Artificial monolayer black phosphorus, so-called phosphorene, has attracted global interest with its distinguished anisotropic, optoelectronic, and electronic properties. Here, we unraveled the shear-induced direct-to-indirect gap transition and anisotropy diminution in phosphorene based on first-principles calculations. Lattice dynamic analysis demonstrates that phosphorene can sustain up to 10% applied shear strain. The bandgap of phosphorene experiences a direct-to-indirect transition when 5% shear strain is applied. The electronic origin of the direct-to-indirect gap transition from 1.54 eV at ambient conditions to 1.22 eV at 10% shear strain for phosphorene is explored. In addition, the anisotropy diminution in phosphorene is discussed by calculating the maximum sound velocities, effective mass, and decomposed charge density, which signals the undesired shear-induced direct-to-indirect gap transition in applications of phosphorene for electronics and optoelectronics. On the other hand, the shear-induced electronic anisotropy properties suggest that phosphorene can be applied as the switcher in nanoelectronic applications.