Electrical conductivity of graphene: A time-dependent density functional theory study

Excitation and propagation of surfaces waves in graphene are analyzed within a frequency band of 1 to 300 THz, and a time domain of 1 to 10 ps. An ab initio approach, based on time dependent density functional theory in linear response regime is used. The key outputs of the simulation are the ab-initio conductance in time and frequency. 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, i.e., at times shorter that 0.1ps, 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.)