|
Abstract:
|
In this dissertation , the applications of many -body physics in neutral bosons and electronic systems in transition metal oxides are discussed . In the first part of the thesis , I will introduce the concepts of Bose condensation , emphasize the significance of the order parameter in superfluids (macroscopic wave function ) , and its consequence such as the emergence of exotic vortex states under rotation . Dated back to the importance of the vortex dynamics in the properties of high T[subscript c] superconductors , people have introduced a dual vortex description to describe the dynamics of charged bosons in a magnetic field . Similarly , the dual description is adapted to the problems of neutral bosons under rotation . Based on that picture , vortices behave like charges in an effective magnetic field which has been known to demonstrate different quantum phases such as Wigner crystal phase , and fractional quantum Hall liquid phases depending on the relative fraction of the number of bosons and vortices . In this work , we would like to address the validity of the picture by low energy effective theory . We can identify the origin of the vortex masse and the parameter regimes in which the vortex dual description is appropriate . In the second part of the dissertation , density functional theory is used to describe the strongly correlated matters with local density approximation and local Hubbard U interaction (LDA+U ) . We are particularly interested in the interface states in the heterojunction systems of two different perovskite oxides . What we found is that the interface states can be engineered to appear in certain transitional metal oxide layers by controlling the number of positive and negative charged layers , leading to the formation of quantum wells in two dimension . This type of systems ignite the hope to search for broken symmetry states in the interface which can be tunable with chemical doping or electric field doping . Even room temperature superconducting state may or may not exist in the interface is still an intriguing issue . |