Polymorphs of two dimensional phosphorus and arsenic: insight from an evolutionary search

Using an evolutionary algorithm, in conjunction with density functional theory (DFT) based electronic, ionic and cell relaxation, we perform an extensive search for the crystal structures of possible two dimensional (2D) allotropes of phosphorus and arsenic. In addition to previously reported allotropes like α, β, γ and δ, we discover four new allotropes, whose cohesive energies differ from that of the ground state (α and β, in the case of P and As, respectively) by merely ∼2-10 meV per atom. In terms of electrical properties, all of them are semiconductors, although the magnitude and nature of the bandgap (direct/indirect) vary considerably. We explain the diversity in terms of the atomic character of the valence and conduction bands of the allotropes. Barring a few exceptions, we find that the effective mass of both the electron and hole has marked anisotropies for most of the allotropes.