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We report the electronic structure and optical absorption spectra ofmonolayer black phosphorus (phosphorene) nanoribbons (PNRs) viafirst-principles simulations. The band gap of PNRs is strongly enhanced byquantum confinement. However, differently orientated PNRs exhibit distinctscaling laws for the band gap vs the ribbon width (w). The band gaps ofarmchair PNRs scale as 1/(w^2), while zigzag PNRs exhibit a 1/w behavior. Thesedistinct scaling laws reflect a significant implication of the band dispersionof phosphorene: electrons and holes behave as classical particles along thezigzag direction, but resemble relativistic particles along the armchairdirection. This unexpected merging of classical and relativistic properties ina single material may produce novel electrical and magnetotransport propertiesof few-layer black phosphorus and its ribbon structures. Finally, therespective PNRs host electrons and holes with markedly different effectivemasses and optical responses, which are suitable for a wide range ofapplications.

Unusual Scaling Laws of the Band Gap and Optical Absorption of Phosphorene Nanoribbons