도체, 부도체 및 초전도체의 앤더스 상전이 현상

Abstract

This thesis includes three parts. In the first part, we investigate the Anderson transition in a 3-dimensional correlated electronic system. In chapter 1, we introduce the basic concept of Anderson transition and Hartree-Fock approximation with its justification. Then, we explain the methods to analyze a disordered system such as multifractal analysis and the properties of entanglement entropy. In chapter 2, we study the role of local moments in the metal-insulator transitions (MIT) in the weak localization regime where the disorder strength is below the critical point (W < Wc). Here, we compare the MIT between long-ranged Coulomb type and short-ranged Hubbard type interactions. We found that while local moments do not affect the MIT when the interaction is long-ranged Coulomb type, the MIT occurs with magnetism in the case of a short-ranged Hubbard type interaction. In chapter 3, we investigate the properties of Anderson-type insulators in the strongly disordered regime where all states are localized (W > Wc). Here, we consider only the short-ranged Hubbard-type interaction and focus on the properties of insulators to study the existence of a many-body localized state (MBL) in a 3- dimensional system. According to the results, two types of Anderson-type insulators are emergent, the phases of which are separated by their interaction strengths. The insulators exhibit differences in the existence of low-energy mobility edges, temperature dependency, magnetization, and entanglement entropy. In the second part, we study the Anderson transition in 2- dimensional disordered superconductors. In Chapter 4, we discuss the delocalization of in-gap state Bogolibov De Gennes (BdG) quasiparticles in a 2-dimensional superconducting system. We reveal that the delocalization of in-gap state BdG quasiparticles is a novel phase transition that is mediated by fluctuations of pairing amplitude. In the appendix of chapter 4, we introduce the basic concept of the tight-binding model in two dimensions and superconductivity in a dirty system. The site-dependent Hartree-Fock approximation for the repulsive interaction and the magnetic field is reviewed focusing on its technical use. Lastly, the role of repulsive interaction is discussed. In the third part, we investigate the distribution of Kondo temperatures due to disorder. In Ch. 5, we study the competition between the Kondo effect and the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. We consider a system that has two Kondo temperatures of two RKKY-coupled magnetic impurities because of different local exchange couplings and the density of states. We found that an initial inequality of the Kondo temperature is enhanced due to the inhomogeneous suppression of the Kondo temperature proportional to the RKKY coupling.