Functionalized Graphene in Quantizing Magnetic Field: The case of bunched impurities

Abstract: Resonant scattering at the atomic absorbates in graphene was investigated recently in relation with the transport and gap opening problems. Attaching an impurity atom to graphene is believed to lead to the creation of unusual zero energy localized electron states. This paper aims to describe the behavior of the localized impurity-induced levels in graphene in a quantizing magnetic field. It is shown that in the magnetic field the impurity level effectively hybridizes with one of the n=0 Landau level states and splits into two opposite-energy states. The new hybridized state is doubly occupied, forming a spin-singlet and reducing the polarization of a Quantum Hall ferromagnet in undoped graphene. Taking into account the electron-electron interaction changes radically the spectrum of the electrons surrounding the impurity, which should be seen experimentally. While existing publications investigate graphene uniformly covered by adatoms, here we address a possibly even more experimentally relevant case of the clusterized impurity distribution. The limit of a dense bunch of the impurity atoms is considered, and it is shown, how such a bunch changes the spectrum and spin polarization of a large dense electron droplet surrounding it. The droplet is encircled by an edge state carrying a persistent current.