Magnetic Properties of Disordered Electron Systems

Abstract

Strongly correlated electron systems show a rich variety of astonishingphysical phenomena. The strong interactions make the theoretical descriptionof these systems a highly non-trivial tast, and even it becomesmore involved if disorder is introduced in the system.This study aims to address the interplay of strong correlations anddisorder in the rst part of this work. It begins with a theoreticalreview of the local moment formation and its quantum uctuationleading the Kondo problem using a mean eld analysis and perturbativescaling theory. A numerical method, or the kernel polynomialmethod (KPM), is introduced to analyze the disorder eect on theKondo eect. It is shown by direct comparisons that KPM resultsgives an excellent agreement with previous numerical and analyticalresults. Remarkably, it strongly supports the recent multifractal analysisof Kondo eect [KMVS12]. KPM is also implemented to study theRKKY interaction in disordered electron systems, after a theoreticalreview of RKKY interaction. Fascinating features of RKKY interactionon disordered graphene are intensively discussed. Semiclassicaldescription of RKKY interaction is presented to give an intuitive understandingand to explain the disorder eect on it. In order to addressthe competition between the Kondo eect and RKKY interaction, thefull distribution of the so-called Doniach criteria, i.e. the ratio betweenthe Kondo temperature and RKKY interaction, is numericallyderived and analyzed. It shows a sharp cuto which allows us to determinethe critical density below which Kondo wins at all positionsin a disordered sample. Based on the analysis of the critical magneticimpurity density, Doniach phase diagram is derived as function of thelocal exchange coupling and intensively discussed.In the second part, analytical study of the optical conductivity and thedensity of states of Kondo lattice systems immersed in massless Diracfermion bath is presented using a slave-boson mean eld theory. Afterthe hybridization, the pseudo-gapt at the center of Dirac fermion bathis shifted into both the upper and the lower quasiparticle band. It isfound that, due to the linear dispersion and the particle-hole symmetryof the Dira fermion, the Kondo insulator gap is observable in the directinterband transition in the optical conductivity. This is in contrast tothe conventional Kondo lattice system.