A comparative study on the edge states in phosphorene quantum dots and rings

Using the tight-binding Hamiltonian approach, we comparatively investigate the energy spectrums of triangular zigzag phosphorene quantum dots (PQDs) and rings (PQRs), as well as their potential applications. In comparison with the outer edge states in the PQD, new extra inner edge states can be produced in the PQR by its internal hole. A transition from the uncoupled to coupled edge states can be induced by decreasing the width between the outer and inner edges of the PQR. Also, the edge states in PQD/PQR are all anisotropically localized in one side, rather than three sides as in triangular graphene quantum dots (QDs) and rings (QRs). Furthermore, the PQD/PQR energy levels can be anisotropically manipulated by the external electric fields and strains, clearly demonstrating their potential applications in field effect transistors or electromechanical devices. In the meanwhile, we also consider the electron probability distributions corresponding to the different energy levels, clearly exposing the characteristics of the PQD/PQR energy levels. The comparison between the asymmetrical triangular PQDs/PQRs and the symmetrical triangular QDs/QRs in graphene should be instructive for understanding the similar triangular QDs/QRs in other two-dimensional layered materials, as well as other types of QDs/QRs of different shapes.