Two-dimensional parabolic Dirac system in the presence of non-magnetic and magnetic impurities

We theoretically investigate the effect of the non-magnetic and magnetic impurities to the 2D parabolic Dirac system. The induced charge density by the charged impuri- ty is obtained by the linear response theory within the random phase approximation. We also detailly calculate the RKKY interaction between two magnetic impurities placed within the 2D sheet of the Dirac materials with isotropic and anisotropic dis- persion. For the anisotropic dispersion, the RKKY interaction is also anisotropic and related to the lattice parameters which can be obtained throuh the DFT calculation or the experiments. The fearures of the RKKY interaction also can be treated as a signature of the topological phase transition as well as the change of Berry curvature. Our results are also illuminating to the study of the static screening and the RKKY interaction of the isotropic or anisotropic 3D Dirac or Weyl systems.