Anomalous STM Images of Resonant States 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 Fano hybridization can occur between the electronic resonance on the substrate and the continuum of conduction states in the STM tip. A maximum of the density of states of the electronic resonance at some energy can then lead to a dip of the STM signal $dI/dV$. Resonances in graphene, known as mid gap states, are good candidates to produce this type of Fano interference. The mid gap states can be produced by local defects or adsorbates and we analyze the cases of top and hollow configurations of adsorbates.