Peierls distortion and electron bands in phosphorus allotropes

A small difference between the rhombohedral phosphorus lattice ($A$-7 phase) and the simple cubic phase as well as between phosphorene and the cubic structure is used in order to construct their quasiparticle band dispersion. We exploit the Peierls idea of the Brillouin zone doubling/folding, which has been previously employed in consideration of semimetals of the V period and IV–VI semiconductors. In a common framework, individual properties of phosphorus allotropes are revealed.