Double band-inversions of bilayer phosphorene under strain and their effects on optical absorption

Strain is a powerful tool to engineer the band structure of bilayer phosphorene. The band gap can be decreased by vertical tensile strain or in-plane compressive strain. At a critical strain, the gap is closed and the bilayer phosphorene is turn to be a semi-Dirac semimetal material. If the strain is stronger than the criterion, a band-inversion occurs and it re-happens when the strain is larger than another certain value. For the zigzag bilayer phosphorene ribbon, there are two edge band dispersions and each dispersion curve represents two degenerate edge bands. When the first band-inversion happens, one of the edge band dispersion disappears between the band-cross points while the other survives, and the latter will be eliminated between another pair of band-cross points of the second band-inversion. The optical absorption of bilayer phosphorene is highly polarized along armchair direction. When the strain is turn on, the optical absorption edge changes. The absorption rate for armchair polarized light is decreased by gap shrinking, while that for zigzag polarized light increases. The band-touch and band-inversion respectively result in the sublinear and linear of absorption curve versus light frequency in low frequency limit.