Tunable edge bands and optical properties in black phosphorus nanoribbons under electric field

For several types of the applied electric field configuration on the normal-zigzag black phosphorus nanoribbon (nZZ-BPNR) we investigate the band structure and the linear optical absorption spectrum, especially for the edge states and the corresponding low-energy absorption peaks. The obtained results show that the applied electric field can not only open another band gap at k=0.5 point, but also can change completely the spacial probabilities of edge states in the two edge bands. The strength of electric field can tune the two band gaps at the Γ point and 0.5 point. Further, one remarkable feature is that the forbidden transition E₁₂ and E₂₁ are allowed. The lowest-excited-energy linear absorption peak E₁₁ originates from the transition between two edge bands at the Γ point. Finally, in comparison with the lowest-excited-energy peaks among various configurations, the second type of electric field configuration can move this peak blue-shift larger than other configurations.