Electronic band structures of group-V two-dimensional materials

We systematically study the electronic properties of two-dimensional group-V materials, i.e. phosphorene, arsenene, antimonene, and bismuthene. The density functional calculations are performed using generalized gradient approximation. We first clarify that the structure is the most stable in the cases of phosphorene and bismuthene and the β structure is the most stable in the cases of arsenene and antimonene. We next analyze the band structures based on group theory. As a result, we find that all the bands are doubly degenerated at the boundaries of the first Brillouin zone in the structures and the degeneracies are due to the symmetry of the materials. The band gaps of the β structures are found to be larger than those of the structures. This tendency in the band gaps is explained based on the fact that the band gap increases as the sp hybridization becomes large. We find that buckling occurs in the structures of antimonene and bismuthene due to the electron transfer from the higher atom to the lower atom.