Anisotropic basic electronic properties of strained black phosphorene

The gap modulation is an intriguing feature of the single-layer black phosphorene (BP) in optoelectronics. In this paper, the uniaxial and biaxial strain effects are systematically investigated to tailor the band gap, Fermi velocity, and effective mass along both armchair (AC) and zigzag (ZZ) directions in BP. The tight-binding model and the Harrison rule propose the electronic phase transitions. In the presence of uniaxial strains, in-plane strains keep the semiconducting phase, while the semiconductor-to-insulator and semiconductor-to-semimetal phase transitions emerge for biaxial strains. Although the anisotropic Fermi velocity introduces critical strains for which the concavity inversion occurs, Fermi velocity increases (decreases) with in-plane (out-of-plane) strain along the AC direction, while it remains constant along the ZZ direction. Further, we found that the heavy (light)-effective mass is related to the ZZ (AC) direction. Moreover, both in-plane and out-of-plane strains lead to effective mass sign-changing due to the concavity inversion of bands. Additionally, the heaviest effective masses are dedicated to critical strains corresponding to the phase transitions after which the concavity inversion of bands emerges. Our results propose interesting information for the strain tuning of electronic properties in BP.