  We perform a comprehensive first-principles study of the electronic
properties of phosphorene nanoribbons, phosphorene nanotubes, multilayer
phosphorene, 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 zigzag
phosphorene nanoribbons (z-PNRs) are metals, regardless of the ribbon width
while armchair phosphorene nanoribbons (a-PNRs) are semiconductors with
indirect bandgaps and the bandgaps are insensitive to variation of the ribbon
width. We find that tensile compression (or expansion) strains can reduce (or
increase) the bandgap of the a-PNRs while an in-plane electric field can
significantly reduce the bandgap of a-PNRs, leading to the
semiconductor-to-metal transition beyond certain electric field. For
single-walled phosphorene nanotubes (SW-PNTs), both armchair and zigzag
nanotubes are semiconductors with direct bandgaps. With either tensile strains
or transverse electric field, similar behavior of bandgap modulation can arise
as that for a-PNRs. It is known that multilayer phosphorene sheets are
semiconductors with their bandgaps decreasing with increasing the number of
multilayers. In the presence of a vertical electric field, the bandgaps of
multilayer phosphorene sheets decrease with increasing the electric field, and
the bandgap modulation is more significant with more layers. Lastly,
heterobilayers of phosporene with a TMDC (MoS2 or WS2) monolayer are still
semiconductors while their bandgaps can be reduced by applying a vertical
electric field as well.
