How good would the conductivity of graphene have to be to make single-layer-graphene metamaterials for terahertz frequencies feasible?

Various terahertz metamaterial devices and concepts involving graphene have been introduced in the literature, however, graphene is either a functional add-on to resonators made from metals with a high electrical conductivity, or it is studied as arrays of relatively simple plasmonic stripes or disks, made from single- or multi-layer graphene. Graphene is never the resonator material of more complex structures such as split-ring resonators because its conductivity is too low. However, for electromagnetic chemical sensors, even a moderate conductivity may be adequate since the response of the metamaterial can be strongly modified by the adsorption of molecules, not only by a change of the dielectric environment, as for conventional metamaterials, but also via a direct change of the conductivity. Here, we consider a prototypical split-ring-resonator consisting of a single layer of patterned graphene on a dielectric, and investigate by simulations its terahertz reflectivity response. The crucial material parameters for device performance are the charge carrier density, controlled by the Fermi energy, and the Drude scattering time. We find that metamaterial behavior becomes interesting if the Drude scattering time of 0.1 ps of standard graphene could be raised to the theoretically accessible value of 0.4-0.5 ps.