  We report the electronic structure and optical absorption spectra of
monolayer black phosphorus (phosphorene) nanoribbons (PNRs) via
first-principles simulations. The band gap of PNRs is strongly enhanced by
quantum confinement. However, differently orientated PNRs exhibit distinct
scaling laws for the band gap vs the ribbon width (w). The band gaps of
armchair PNRs scale as 1/(w^2), while zigzag PNRs exhibit a 1/w behavior. These
distinct scaling laws reflect a significant implication of the band dispersion
of phosphorene: electrons and holes behave as classical particles along the
zigzag direction, but resemble relativistic particles along the armchair
direction. This unexpected merging of classical and relativistic properties in
a single material may produce novel electrical and magnetotransport properties
of few-layer black phosphorus and its ribbon structures. Finally, the
respective PNRs host electrons and holes with markedly different effective
masses and optical responses, which are suitable for a wide range of
applications.
