Summary of This Book

In the present study, we studied microscopic origin of SC and multipole phase in SCES in a unified way considering many body effects beyond RPA+ME theory. Until recently, it was widely believed that the basic properties of SC states in SCES are qualitatively well understood within conventional RPA+ME theory. However, recent experiments revealed that RPA+ME theory fails in several SCES, such as Fe-based and HF superconductor. Thus, new microscopic theory is required to solve the problem. Here, we focused on significant roles of VC due to many body effects. It was revealed that violation of RPA+ME theory occurs especially in multi-orbital and multipole systems.