Electrically Tunable Quasi-Flat Bands, Conductance and Field Effect Transistor in Phosphorene

Phosphorene, a honeycomb structure of black phosphorus, was isolated recently. We investigate electric properties of phosphorene nanoribbons based on the tight-binding model. A prominent feature is the presence of quasi-flat edge bands entirely detached from the bulk band. We explore the mechanism of the emergence of the quasi-flat bands analytically and numerically from the flat bands well known in graphene by a continuous deformation of a honeycomb lattice. The quasi-flat bands can be controlled by applying in-plane electric field perpendicular to the ribbon direction. The conductance is switched off above a critical electric field, which acts as a field-effect transistor. The critical electric field is anti-proportional to the width of a nanoribbon. This results will pave a way toward nanoelectronics based on phosphorene.