  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.
