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 transitionallowed.The lowest-excited-energy linear absorption peakfrom 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.
Connecting one armchair carbon nanotube（CNT） to several zigzag graphene nanoribbons（ZGNRs） we find that the topologically-protected edge states of ZGNRs and the massless Dirac particle inherited from CNT still hold from the analysis of the band structure and the edge state. Furthermore, the lowest conductance step at the valley bottom increases proportionally with increasing the number of ZGNR wings. A novel conductance step of a peak occurs in the valley, which is two steps higher than the lowest step at the valley bottom. In addition, with increasing the number of ZGNR wings the width of the novel conductance step becomes narrow.
Connecting three zigzag graphene nanoribbons（ZGNRs） together through the sp^3 hybrid bonds forms a star-like ZGNR（S-ZGNR）. Its band structure shows that there are four edge states at k = 0.5, in which the three electrons distribute at three outside edge sites, and the last electron is shared equally（50%） by two sites near the central site. The lowest conductance step in the valley is 2, two times higher than that of monolayer ZGNR（M-ZGNR）. Furthermore, in one quasithree-dimensional hexagonal lattice built, both of the Dirac points and the zero-energy states appear in the band structure along the z-axis for the fixed zero k-point in the x-y plane. In addition, it is an insulator in the x-y plane due to band gap 4 eV, however, for any k-point in the x-y plane the zero-energy states always exist at kz = 0.5.
