Scaling laws for band gaps of phosphorene nanoribbons: A tight-binding   calculation
  In this study, we analyze the band structure, the state characterization, and electronic transport of monolayer black phosphorus (phosphorene) zigzag nanoribbons (zPNRs) and armchair nanoribbons (aPNRs), using five-parameter tight-binding (TB) approximation. In zPNRs, the ratio of the two dominant hopping parameters indicates the possibility of a relativistic dispersion relation and the existence of a pair of separate quasi-flat bands at the Fermi level. Moreover, the corresponding states are edge localized if their bands are well separated from the valence and conduction bands. We also investigated the scaling laws of the band gaps versus ribbon widths for the armchair and zigzag phosphorene nanoribbons. In aPNRs, the transverse electric field along the ribbon width enhances the band gap closure by shifting the energy of the valence and conduction band edge states. For zPNRs, a gap occurs at the middle of the relatively degenerate quasi-flat bands; thus, these ribbons are a promising candidate for future field-effect transistors. 
Esmaeil Taghizadeh Sisakht, Mohammad H. Zare, and Farhad Fazileh
cond-mat.mes-hall