Structural, vibrational, and electronic properties of single-layer hexagonal crystals of group IV and V elements

Using first-principles density functional theory calculations, we investigate a family of stable two-dimensional crystals with chemical formula A(2)B(2), where A and B belong to groups IV and V, respectively (A = C, Si, Ge, Sn, Pb; B = N, P, As, Sb, Bi). Two structural symmetries of hexagonal lattices P (6) over bar m2 and P (3) over bar m1 are shown to be dynamically stable, named as alpha- and beta-phases correspondingly. Both phases have similar cohesive energies, and the a phase is found to be energetically favorable for structures except CP, CAs, CSb, and CBi, for which the beta phase is favored. The effects of spin-orbit coupling and Hartree-Fock corrections to exchange correlation are included to elucidate the electronic structures. All structures are semiconductors except CBi and PbN, which have metallic character. SiBi, GeBi, and SnBi have direct band gaps, whereas the remaining semiconductor structures have indirect band gaps. All structures have quartic dispersion in their valence bands, some of which make the valence band maximum and resemble a mexican-hat shape. SnAs and PbAs have purely quartic valence band edges, i.e., E - alpha k(4), a property reported for the first time. The predicted materials are candidates for a variety of applications. Owing to their wide band gaps, CP, SiN, SiP, SiAs, GeN, GeP can find their applications in optoelectronics. The relative band positions qualify a number of the structures as suitable for water splitting, where CN and SiAs are favorable at all pH values. Structures with quartic band edges are expected to be efficient for thermoelectric applications.