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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 nonrelativistic particles along the zigzag direction but resemble relativistic particles along the armchair direction. This unexpected merging of nonrelativistic 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 absorption spectra, which are suitable for a wide range of applications.
Tran et al. (Mon,) studied this question.