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We consider charge transport across a finite graphene flake with a circularantidot defined in its center. The flake is connected to thin metallic armchairnanoribbons and the study covers the energy range within the neighborhood ofthe neutrality point. We solve the scattering problem using the tight-bindingHamiltonian and find that conductance of the system is non-zero only nearnarrow resonances which are quasi-bound in either the entire cavity or theantidot itself. We demonstrate that the scanning probe technique can be usedfor the purpose of determination whether the state is localized within theantidot or in the entire cavity. We indicate that the potential of theperturbation shifts the position of the resonances and that the shifts arerelated to the localization of the scattering probability density. Theresonance lifetime can be both decreased or increased as the perturbationintroduced by the probe interferes with the current vortices inside theantidot.

Imaging the localization of the quasi-bound states in graphene antidots