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Phosphorene (a monolayer of black phosphorus) recently spurred much attention due to its potential for application. We notice there are two types of zigzag edge and two types of armchair edge for phosphorene lattice. We study the winding number of various types of edge of phosphorene ribbons and conclude that, besides on the typical zigzag edge, the flat zero-energy edge band can be found in the ribbon...
We investigate the edge bands of the relaxed phosphorene edges. The edge relaxation is modeled by letting the outmost bonds be different. By treating the relaxed hopping energy as a parameter, we observe the phase transition for the edge band appearance in the bulk gap. The analytical expression of the relaxed hopping for the phase transition is obtained by means of tight-binding parameters.
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