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Magnetic Properties of Disordered Electron Systems

Magnetic Properties of Disordered Electron Systems
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Strongly correlated electron systems show a rich variety of astonishing physical phenomena. The strong interactions make the theoretical description of these systems a highly non-trivial tast, and even it becomes more involved if disorder is introduced in the system. This study aims to address the interplay of strong correlations and disorder in the rst part of this work. It begins with a theoretical review of the local moment formation and its quantum uctuation leading the Kondo problem using a mean eld analysis and perturbative scaling theory. A numerical method, or the kernel polynomial method (KPM), is introduced to analyze the disorder e ect on the Kondo e ect. It is shown by direct comparisons that KPM results gives an excellent agreement with previous numerical and analytical results. Remarkably, it strongly supports the recent multifractal analysis of Kondo e ect [KMVS12]. KPM is also implemented to study the RKKY interaction in disordered electron systems, after a theoretical review of RKKY interaction. Fascinating features of RKKY interaction on disordered graphene are intensively discussed. Semiclassical description of RKKY interaction is presented to give an intuitive understanding and to explain the disorder e ect on it. In order to address the competition between the Kondo e ect and RKKY interaction, the full distribution of the so-called Doniach criteria, i.e. the ratio between the Kondo temperature and RKKY interaction, is numerically derived and analyzed. It shows a sharp cuto which allows us to determine the critical density below which Kondo wins at all positions in a disordered sample. Based on the analysis of the critical magnetic impurity density, Doniach phase diagram is derived as function of the local exchange coupling and intensively discussed. In the second part, analytical study of the optical conductivity and the density of states of Kondo lattice systems immersed in massless Dirac fermion bath is presented using a slave-boson mean eld theory. After the hybridization, the pseudo-gapt at the center of Dirac fermion bath is shifted into both the upper and the lower quasiparticle band. It is found that, due to the linear dispersion and the particle-hole symmetry of the Dira fermion, the Kondo insulator gap is observable in the direct interband transition in the optical conductivity. This is in contrast to the conventional Kondo lattice system.
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