Stacking sequences of black phosphorous allotropes and the corresponding few-layer phosphorenes

Possible bulk black phosphorus (BP) allotropes are constructed based on single-layer BP with various stacking sequences. Our stacking algorithm shows that there are eight possible allotropes with two stacking layers in their unit cells possessing relatively high symmetries, and six of them are retained after structural relaxation using a van der Waals correction of optB88-vdW. The AF, AG, and AH bulk structures are presented for the first time. The structural relationship of these configurations has been explained via an interlayer slipping process. The total energy of the AF allotrope is closest to the most stable bulk BP structure (AB stacking) among all explored 2-layer stacked bulk structures. The calculated band structure of the AF allotrope using HSE06 shows a direct band gap of 0.48 eV with anisotropic electronic structures. We also presented six possible BP allotropes with three stacking layers in their unit cells. The newly reported AAF and ABC stacked structures show semiconducting and metallic features, respectively. After the bulk structures were explored, we further built the corresponding few-layer phosphorene structures and investigated their electronic properties. The results show that all the few-layer phosphorenes show semiconducting features. The AE, AAE, and AEA phosphorenes have indirect band gaps while the other explored phosphorenes possess direct band gaps located at the Γ point.