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Theory for STM images of resonances in the near-field regime: application to adsorbates and local defects on graphene

We analyze the STM current through electronic resonances on a substrate as a function of tip-surface distance. We show that when the tip approaches the surface a maximum of the density of states of the electronic resonance at some energy can lead to a dip of the STM signal dI/dV. This phenomenon is a Fano effect resulting from the coupling of the electronic states of the STM tip with the resonance. In graphene such resonances can be produced by local defects or adsorbates and we analyze the cases of top and hollow configurations of adsorbates.