Localised magneto‐optical collective excitations of impure graphene

We study optically‐induced collective excitations of graphene in the presence of a strong perpendicular magnetic field and a single impurity. We determine the energies and absorption strengths of these excitations, which become localised on the impurity. Two different types of impurity are considered i. the long‐range Coulomb impurity, ii. a δ‐function impurity located at either an A or B graphene sublattice site. Both impurity types result in some bound states appearing both above and below the magnetoplasmon continuum, although the effect of the short‐range impurity is less pronounced. The dependence of the energies and oscillator strengths of the bound states on the filling factor is investigated.