Electromagnetic characterization of graphene and graphene nanoribbons via ab-initio permittivity simulations

Excitation and propagation of surfaces waves in graphene and graphene nanoribbons are analyzed, within a frequency band of 1 to 300 THz, based on time dependent density functional theory, in linear response regime. The key outputs of the simulation is the ab-initio complex impeance of the materials. This is shown to tend to a continuous integral relations in graphene, when the valence and conduction bands is treated within the conical approximation, in agreement with a widely used construction derived from the Kubo formula. Non negligible differences are observed between the ab-initio and continuous methods at frequencies larger than a few tens of THz, where the conical approximation reaches its limits of validity. The main conclusion of the study is that a novel conductivity concept is introduced, which represents a fundamental improvement with respect to some commonly used methods in electromagnetic simulations, working at THz frequencies. These tools may open the way to properly analyze graphene related materials, hethero-structures and interfaces.