Theoretical Investigations On The Effects Of Impurities In Two Kinds Of Strongly Correlated Electron Systems

The effects of impurity and vacancy always attract much interest in the investi-gation of strongly correlated system. In this thesis we study theoretically the impurity effect in high-Tc cuprates and strongly correlated topological insulator. As supercon-ducting phase emerges by doping holes or electrons on Mott insulator, the dynamic of a single hole or electron in an antiferromagnetic Mott insulator is highly non-trivial. On the other hand, novel phenomena arise on the Kane-Mele-Hubbard model with the special topological features and interface states. As a tiny interface, vacancy on lattice show a distinct response in this model. Therefore, this thesis is consist of two parts as follows:1. Motivated by the recent atomic-scale scanning tunneling microscope obser-vation for a spatially localized in-gap state in an electron doped Mott insulator, we calculate the local density of state of the Hubbard model on the square lattice using the cluster perturbation theory. An in-gap state is found to exist below the upper Hubbard band around the dopant lattice site, which is consistent with the STM measurements. The emergence of this local in-gap state is accompanied with a rapid reduction of the double occupancy of electrons. A similar in-gap state is also found to exist on the triangular lattice. These results suggest that the in-gap state is driven by the strong correlation effect associated with the Mott transition and is an inherent feature of Mott insulators independent of the lattice structure.2. The local magnetism induced by vacancies in the presence of the spin-orbit interaction is investigated based on the half-filled Kane-Mele-Hubbard model on the honeycomb lattice. Using the self-consistent mean-field theory, we find that the spin-orbit coupling will enhance the localization of the spin moments near a single vacancy. We further study the magnetic structures along the zigzag edges formed by a chain of vacancies. The spin-orbit coupling tends to suppress the counter-polarized ferrimagnet-ic order on the upper and lower edges, because of the open of the spin-orbit gap. As a result, in the case of the balance number of sublattices, it will suppress completely this kind of ferrimagnetic order. But, for the imbalance case, a ferrimagnetic order along both edges exists because additional zero modes will not be affected by the spin-orbit coupling.