Impurity States on the Kagome Lattice Using Green's Function Method

The kagome lattice is a 2D lattice that has been of recent interest owing to its graphene-like band structure, the existence of flat band states and exotic quasiparticle excitations. Materials hosting the kagome lattice such as the rare-earth compound RCo$_5$ and the herbertsmithites have been recently synthesized and efforts have been made to change the Fermi energy to the Dirac-like point by introducing impurities into this system. In this work, we study the electronic states introduced by impurities in the system by applying the Green's function approach within a tight-binding model Hamiltonian. The impurities introduce localized states close to the Dirac point, in many ways similar to graphene, which will be discussed.