Nanoantenna properties of graphene membrane. Quantum theory

The graphene membrane irradiated by weak activating alternative electric field in terahertz range was considered. The quantum approach based on the time-dependent density matrix method was used. The exact solution was obtained for graphene membrane density matrix equation in linear on the external field approximation. The graphene electromagnetic response was studied i.e. the formulae for the induced current and conductivity were found and analyzed neglecting loss. The obtained formula for the conductivity showed that the graphene membrane was an oscillating contour and its fundamental eigen frequency coincided with a singularity point of the conductivity. This formula allowed us to calculate the graphene membrane inductivity and the capacitance. So the graphene membrane could be used as an antenna or a transistor. It was shown that its eigen frequency could be tuned by doping as its value was found to depend on electrons concentration. It was obtained that the eigen frequency could be tuned in a rather large frequency range 1-100 terahertz as electrons concentration in graphene may differ considerably. The found dependence on concentration correlates with experiments. It would be useful to take the obtained results into account when constructing devices containing graphene membrane nanoantenna allowing wireless communications among nanosystems. This could be promising research area of energy harvesting applications.