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Title:Theoretical study of Kondo effect and related transport properties in topological insulator systems
Author(s):Xin, Xianhao
Director of Research:Stone, Michael
Doctoral Committee Chair(s):Hughes, Taylor L.
Doctoral Committee Member(s):Cooper, Lance; Makins, Naomi C
Department / Program:Physics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):Topological Insulator
Kondo Effect
Abstract:This thesis presents theoretical studies of the Kondo effect and related transport properties in topological insulator systems. The thesis mainly covers two topics: the Kondo effect on the surface of a bulk topological insulator material and the Kondo effect in a topological insulator quantum dot. Other relevant background knowledge and theoretical techniques for the transport calculations are also discussed in the thesis. For the first topic, we investigate the role of magnetic impurities in the transport properties of a three dimensional topological insulator's surface states. First, we combine the second-order perturbation theory and the Boltzmann transport equation to calculate the magnetically induced resistivity in a topological insulator. Our result shows a non-perturbative behavior when conduction electrons and magnetic impurities' spins are antiferromagnetically coupled. The surface resistivity is found to display an oscillatory rather than isotropic behavior compared to the conventional Kondo effect. Both the variational method and renormalization group (RG) analysis are employed to compute the Kondo temperature, through which the non-perturbative behavior is confirmed. We further study the RG flows and demonstrate that the RG trajectories eventually flow into a strong coupling regime if the coupling is antiferromagnetic. This work is motivated by the recent transport experiments, in which surface currents were detected in topological insulators. The calculation is shown to be qualitatively consistent with the low temperature dip observed in the experimental R − T curve, and it might be one of the possible origins of the dip. For the second main topic, we investigate theoretically the nonequilibrium transport properties of a topological insulator quantum dot (TIQD) in the Coulomb blockade and Kondo regime. An Anderson impurity model is applied to a TIQD system coupled to two external leads, and we show that the model realizes the spin-orbital Kondo effect at the Dirac point where the edge states are not split by a finite-size effect, leading to an additional SU(4) symmetry because of the presence of strong mixture among four internal degrees of freedom. In a more realistic situation where the degeneracy is lifted due to the finite-size effect, we demonstrate that there is a richer structure in transport measurements. We illustrate a continuous crossover from four (spin and orbital) Coulomb peaks with large interpair spacing and small intrapair spacing to a double-peak structure in the local density of states (LDOS) as increasing the hybridization strength �� within the Coulomb blockade regime. When temperature falls below the Kondo temperature TK, four Kondo peaks show up in the nonequilibrium LDOS. Two of them are located at the chemical potential of each lead, and the other two are shifted away from the chemical potential by an amount proportional to the TIQD’s bare energy level, leading to a triple-peak structure in the differential conductance when a bias voltage is applied.
Issue Date:2015-11-30
Rights Information:Copyright 2015 Xianhao Xin
Date Available in IDEALS:2016-07-07
Date Deposited:2016-05

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