The Study of Transition Metal Oxides using Dynamical Mean Field Theory

In this thesis, we study strong electron correlation in transition metal oxides. In the systems with large Coulomb interaction, especially the on-site interaction, electrons are much more correlated and cannot be described using traditional one-electron picture, thus the name "strongly correlated systems". With strong correlation, there exists a variety of interesting phenomena in these systems that attract long-standing interests from both theorists and experimentalists. Transition metal oxides (TMOs) play a central role in strongly correlated systems, exhibiting many exotic phenomena. The fabrication of heterostructures of transition metal oxides opens many possible directions to control bulk properties of TMOs as well as revealing physical phases not observed in bulk systems. Dynamical mean-field theory (DMFT) emerges as a successful numerical method to treat the strong correlation. The combination of density functional and dynamical mean-field theory (DFT+DMFT) is a prospective ab initio approach for studying realistic strongly correlated materials. We use DMFT as well as DFT+DMFT methods as main approaches to study the strong correlation in these materials. We focus on some aspects and properties of TMOs in this work. We study the magnetic properties in bulk TMOs and the possibility of enhancing the magnetic order in TMO heterostructures. We work on the metallic/insulating behaviors of these systems to understand how the metal-insulator transition depends on the intrinsic parameters of materials. We also investigate the effect of a charged impurity to the neighborhood of a correlated material, which can be applied, for example, to the study of muon spin relaxation measurements in high-Tc superconductors.