| The purpose of this thesis is the theoretical study of the high temperature superconductors. Among many high temperature superconducting materials, the study is focused on the cuprates and the recently discovered iron-based superconductors (oxypnictides). High temperature superconductor theory has been one of the frontiers in condensed matter physics in the two decades since its discovery. We do not focus on the mechanism of how the superconductivity arises in these materials. Rather, we pay more attention to the several characteristic features in the high temperature superconductors. Contrary to the conventional low transition temperature superconductors, the high temperature superconductors are strongly correlated electronic systems in which many types of low energy orders are present. These orders compete with the superconductivity. Furthermore, the high temperature superconductors reveal a non-trivial pairing symmetry, and to identify this symmetry is the goal of a significant number of ongoing research projects.;In this thesis, first, we study the physics of the universal phenomena in cuprates from the point of view of the competing order. To this purpose, we propose a new order to understand the physics in the disordered states and at the temperature above Tc, and review the general characters of this order, emphasizing the symmetry and order wave-vectors. Second, we investigate the symmetry of the superconducting order and its relation to the magnetic properties of the iron-based superconductors. |
