Coupling and manipulation of edge states in multilayer phosphorene nanoribbons

We investigate the couplings among the edge states of the normal zigzag and skewed armchair multilayer phosphorene nanoribbons, as well as the effect of the electric field on the corresponding energy levels, by using the tight-binding Hamiltonian approach. It is found that there appear different transitions from the coupled to uncoupled edge states in the normal zigzag and skewed armchair nanoribbons with the increasing of the nanoribbon width, which is fundamentally attributed to the edge asymmetry of the multilayer phosphorene nanoribbons. Moreover, the energy bands of the multilayer phosphorene nanoribbons can be effectively adjusted by applying the perpendicular electric field. Therefore, this research should be thought of as a useful reference for determining the width, the edge types, and the layer numbers of the nanoribbons in manipulating the properties of the multilayer phosphorene nanoribbons.