  We present an ab-initio investigation of effects of shear strain on band
structure and electronic properties of 2D phosphorene. We carried out DFT
calculations to determine the shear stress as a function of shear strain and
found the monolayer phosphorene has ultimate strength at shear strain 30% and
35% in armchair and zigzag directions, respectively, and it was also found that
the monolayer extends in z direction on applying shear strain in both
directions. Additionally, we derived band structures of phosphorene along both
directions under shear strain and have shown that band gap in phosphorene
decreases along both directions and that phosphorene shows a semi-metal nature
on applying shear strain of magnitude 30% in both directions. The electrical
conductivity of phosphorene was estimated by effective mass along zigzag and
armchair directions and it is shown that the electrical conductivity is far
higher along armchair direction, and that with increasing shear strain
conductivity increases along armchair, up to ultimate strength, and zigzag
directions.
