The dynamical conductance of graphene tunnelling structures

The dynamical conductances of graphene tunnelling structures were numerically calculated using the scattering matrix method with the interaction effect included in a phenomenological approach. The overall single-barrier dynamical conductance is capacitative. Transmission resonances in the single-barrier structure lead to dips in the capacitative imaginary part of the response. This is different from the ac responses of typical semiconductor nanostructures, where transmission resonances usually lead to inductive peaks. The features of the dips depend on the Fermi energy. When the Fermi energy is below half of the barrier height, the dips are sharper. When the Fermi energy is higher than half of the barrier height, the dips are broader. Inductive behaviours can be observed in a double-barrier structure due to the resonances formed by reflection between the two barriers.