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We study the effect of resonant scatterers on the local density of states ina rectangular graphene setup with metallic leads. We find that the density ofstates in a vicinity of the Dirac point acquires a strong position dependencedue to both metallic proximity effect and impurity scattering. This effect mayprevent uniform gating of weakly-doped samples. We also demonstrate that even asingle-atom impurity may essentially alter electronic states at low-doping ondistances of the order of the sample size from the impurity.

Metallic proximity effect in ballistic graphene with resonant scatterers