We have investigated a new feature of impurity cyclotron resonances common to various localized potentials of graphene. A localized potential can interact with a magnetic field in an unexpected way in graphene. It can lead to formation of anomalous boundstates that have a sharp peak with a width $R$ in the probability density inside the potential and a broad peak of size magnetic length $ell$ outside the potential. We investigate optical matrix elements of anomalous states, and find that they are unusually small and depend sensitively on magnetic field. The effect of many-body interactions on their optical conductivity is investigated using a self-consistent time-dependent Hartree-Fock approach (TDHFA). For a completely filled Landau level we find that an excited electron-hole pair, originating from the optical transition between two anomalous impurity states, is nearly uncorrelated with other electron-hole pairs, although it displays a substantial exchange self-energy effects. This absence of correlation is a consequence of a small vertex correction in comparison to the difference between renormalized transition energies computed within the one electron-hole pair approximation. However, an excited electron-hole pair originating from the optical transition between a normal and an anomalous impurity states can be substantially correlated with other electron-hole states with a significant optical strength.
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