Phosphorene nanoribbons, phosphorus nanotubes, and van der Waals multilayers

We perform a comprehensive first-principles study of the electronic properties of phosphorene nanoribbons, phosphorus nanotubes, multilayer phosphorene sheets, and heterobilayers of phosphorene and two-dimensional (2D) transition-metal dichalcogenide (TMDC) monolayer. The tensile strain and electric-field effects on electronic properties of low-dimensional phosphorene nanostructures are also investigated. Our calculations show that the bare zigzag phosphorene nanoribbons (z-PNRs) are metals regardless of the ribbon width, whereas the bare armchair phosphorene nanoribbons (a-PNRs) are semiconductors with indirect bandgaps and the bandgaps decrease with increasing ribbon width. We find that compressive (or tensile) strains can reduce (or enlarge) the bandgap of the bare a-PNRs while an in-plane electric field can significantly reduce the bandgap of the bare a-PNRs, leading to the semiconductor-to-metal transition beyond certain electric field. For edge-passivated PNR by hydrogen, z-PNRs become semiconductor with nearly direct bandgaps and a-PNRs are still semiconductor but with direct bandgaps. The response to tensile strain and electric field for the edge-passivated PNRs is similar to that for the edge-unpassivated (bare) a- PNRs. For single-walled phosphorus nanotubes, both armchair and zigzag nanotubes are semiconductors with direct bandgaps. With either tensile strains or transverse electric field, behavior of bandgap modulation similar to that for a-PNRs can arise. It is known that multilayer phosphorene sheets are semiconductors whose bandgaps decrease with an increase in the number of multilayers. In the presence of a vertical electric field, the bandgaps of multilayer phosphorene sheets decrease with increasing electric field and the bandgap modulation is more significant with more layers. Lastly, heterobilayers of phosphorene (p-type) with an n-type TMDC (MoS₂ or WS₂) monolayer are still semiconductors while their bandgaps can be reduced by applying a vertical electric field as well. We also show that the combined phosphorene/MoS₂ heterolayers can be an effective solar cell material. Our estimated power conversion efficiency for the phosphorene/MoS₂ heterobilayer has a theoretical maximum value of 17.5%.