安德森－哈伯德模型在拓撲絕緣體中的研究

In this project, I intend to study the Anderson-Hubbard model and the relevant experiments, mainly on transition metal oxide. Doping in transition metal oxide introduces strong disorder, and the role played by these disorders is not clear. The V-shape depletion of the density of states near the Fermi energy in the Anderson-Hubbard model indicates the kinetic driven scattering process in strong interaction limit. The spin and charge fluctuations are also responsible for the formation of the pseudogap. We also plan to include the longer-range interorbital interactions term to study the contribution of the spin and charge fluctuations. Moreover, experiments are performed at finite temperature which adds an extra energy scale to the problem. The recent proposal of a many-body localization transition at nonzero temperature underscores the richness of the phase space. One of the goals of this project is to explore the interplay of strong interactions, disorder, kinetic energy and temperature in the Anderson-Hubbard model. Furthermore, in some transition metal oxides, the 3d orbitals enhance the on-site Coulomb repulsion and typically dominate the energy scale where the spin orbit interactions are small compared to the on-site electron-electron interaction. The strong spin orbit coupling results from the large atomic numbers of heavy transition elements. Thus, for materials with 4d or 5d electrons, one expects the appearance of novel phases due to the spin orbit coupling. It has been proposed that the topological insulator may appear in the strongly electron-electron correlated systems, for instance, in 4d or 5d transition metal oxides. To extend the Hubbard model in topological insulator, we investigate the role of disorders in the context of the spin orbit interactions and the strong electronic correlations. The Anderson-Hubbard model is the good candidate to explore the topological insulating phases.