Impurity assisted nanoscale localization of plasmonic excitations in graphene

The plasmon modes of pristine and impurity doped graphene are calculated, using a real-space theory which determines the non-local dielectric response within the random phase approximation. A full diagonalization of the polarization operator is performed, allowing the extraction of all its poles. It is demonstrated how impurities induce the formation of localized modes which are absent in pristine graphene. The dependence of the spatial modulations over few lattice sites and frequencies of the localized plasmons on the electronic filling and impurity strength is discussed. Furthermore, it is shown that the chemical potential and impurity strength can be tuned to control target features of the localized modes. These predictions can be tested by scanning tunneling microscopy experiments.