Electrical polarizability of a local chemical potential interruption in a Graphene layer

The chemical potential of a Graphene layer can be locally interrupted by electrostatic or chemical doping. If the interrupted domain is sufficiently small then an interruption´s polarizability can be defined and calculated. Unlike the conventional polarizability which is defined directly via a particle´s dipole response, here it is defined via the induced currents in the interruption itself and in its surrounding Graphene layer. The result have potential applications in the modeling and design of many one-atom-thick, tuneable two-dimensional metamaterials, optical sub-diffractive waveguides and more.