▎ 摘　　要

We considered a graphene membrane irradiated by a weak activating periodic electric field in the terahertz range. We used the quantum approach based on the time-dependent density matrix method to analyze the graphene electromagnetic response. For this goal the exact solution was found for the graphene membrane density matrix equation in linear approximation on the external field. On this basis the induced current was studied and then we obtained the formula for quantum conductivity as a function of external field frequency and temperature. The found formula for the conductivity corrected the one obtained in 2007 by Gusynin, Sharapov and Carbotte (Phys. Rev. B, 75 (2007) 165407). The corrected formula allowed to see that the graphene membrane was an oscillating contour, its fundamental eigenfrequency coinciding with a singularity point of the conductivity. The obtained formula allowed us also to calculate the graphene membrane quantum inductivity and capacitance. So in effect we demonstrated that the graphene membrane could be used as an antenna or a transistor. It was shown also that its eigenfrequency could be tuned by doping as its value was found to depend on electrons concentration. It was obtained that the eigenfrequency could be tuned in a rather large terahertz-infrared frequency range as electrons concentration in graphene may differ considerably. The found dependence on concentration is consistent with experiments. The presented formula for conductivity can be used to correct the SPPs Dispersion Relation and for the description of radiation process. It would be useful to take the obtained results into account when constructing devices containing a graphene membrane nanoantenna. Such project could make it possible to create wireless communications among nanosystems. This would be a promising research area of energy harvesting applications. Copyright (C) EPLA, 2016