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

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