Topological origin of quasi-flat edge band in phosphorene

Phosphorene, a honeycomb structure of black phosphorus, was isolated recently. The band structure is highly anisotropic, where the k x direction is Dirac-like and the k y direction is Schrödinger-like. A prominent feature is the presence of a quasi-flat edge band entirely detached from the bulk band in phosphorene nanoribbons. We explore the mechanism of the emergence of the quasi-flat band by employing the topological argument invented to explain successfully the flat band familiar in graphene. The quasi-flat band 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.