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In this paper, we develop a theory of edge effects in graphene for itsapplications to nanoantennas in the terahertz, infrared, and visible frequencyranges. Its characteristic feature is selfconsistence reached due theformulation in terms of dynamical conductance instead of ordinary used surfaceconductivity. The physical model of edge effects is based on using the conceptof Dirac fermions. The surface conductance is considered as a generalsusceptibility and is calculated via the Kubo approach. In contrast withearlier models, the surface conductance becomes nonhomogeneous and nonlocal.The spatial behavior of the surface conductance depends on the length of thesheet and the electrochemical potential. Results of numerical simulations arepresented for lengths in the range of 2.1-800 nm and electrochemical potentialsranging between 0.1-1.0 eV. It is shown that if the length exceeded 800 nm, ourmodel agrees with the classical Drude conductivity model with a relatively highdegree of accuracy. For rather short lengths, the conductance usually exhibitsspatial oscillations, which absent in conductivity and strongly affect theproperties of graphene based antennas. The period and amplitude of such spatialoscillations, strongly depend on the electrochemical potential. The new theoryopens the way for realizing electrically controlled nanoantennas by changingthe electrochemical potential may of the gate voltage. The obtained results maybe applicable for the design of carbon based nanodevices in modern quantumtechnologies.

Theory of Edge Effects and Conductance for Applications in Graphene-based Nanoantennas