Even–odd effect of electric and optical properties for antiferromagnetic zigzag phosphoene nanoribbons under an electric field

Abstract

The study on the electronic especially optical properties of zigzag-edged phosphorene nanoribbons (ZPNRs) in an antiferromagnetic state has been rarely involved. Here we theoretically study the electronic and optical properties of a ZPNR with N chains (N-ZPNR) modulated by a vertical electric field (VEF). Within the Hubbard model Hamiltonian combined with the self-consistent calculation, and by adopting the Green’s function method, we obtain the band structure and corresponding conductance for the system. The corresponding optical absorption spectrum is further obtained based on the Kubo formula. It is interesting to find that there is an even–odd effect on the electronic and optical properties of N-ZPNR induced by the VEF, which may fundamentally originate from the parity of the wavefunctions. The VEF lifts the degeneracy of the two edge bands for 12-ZPNR, but it only bends and shifts the two edge bands without lifting the spin degeneracy for 13-ZPNR. We further present the spatial distribution of the corresponding wavefunction to understand this even–odd effect more intuitively. As expected, the VEF can separate the spin-up and -down optical absorption for 12-ZPNR, but it does not break the spin degeneracy of the optical absorption for 13-ZPNR. Our results may provide a further understanding on the electronic and optical properties of N-ZPNR with an antiferromagnetic state, and may be useful to identify the even–odd property of ZPNR samples by detecting the optical absorption in experiment.