Abstract

This thesis contributes to the understanding of impurity models. It is divided into two main parts, with a general introduction given in Part I and the research related to it presented in Part II, with the second part being subdivided into two main projects. In the first project, the influence of two many-body effects, the Kondo effect and the Fermi edge singularity, on the absorption and emission spectra of self-assembled quantum dots (QDs) is examined. Whereas the Kondo effect so far was always examined with transport experiments, we show that it has been observed with optical methods for the first time, by comparing experimental data for the absorption line shapes of QDs to calculations with the numerical renormalization group. We continue by examining a QD with strong optical coupling of the energy levels. The resulting interplay of Rabi-oscillations and Kondo effect leads to a new many-body state, a secondary, outer Kondo effect, with Kondo-like correlations between the spin-Kondo and the trion state. The last work regarding optics at QDs addresses the Fermi edge singularity. We show that for QDs this phenomenon can be described numerically on a quantitative level. The second project concerns transport properties of impurity models. First, we present a comprehensive study of the Kondo effect for an InAs-nanowire QD, a system for which the Kondo effect was observed only a few years ago. The second study regarding transport concerns the Kondo effect in bulk metals with magnetic impurities. Although nowadays the Kondo effect is often studied with QDs, it was discovered for iron impurities in noble metals like gold and silver. However, it was unknown for a long time which exact realization of Kondo model describes these systems. We identify the model by comparing numerical calculations for the magnetoresistivity and the dephasing rate for different models to experimental results. The third work about transport concerns the phenomenon that for a fixed type of Kondo model quantities like the magnetoresistivity or the conductivity, respectively, can be scaled onto a universal curve for different parameters, when energies are rescaled with the the Kondo temperature $T_K$, since it is the only relevant low energy scale of the problem. For finite bandwidth, however, different definitions of $T_K$ (which coincide in the limit of infinite bandwidth) lead to different $T_K$-values. We show that with a very common definition of $T_K$, finite bandwidth, which is always present at numerical calculations, can deteriorate the universality of rescaled curves, and we offer an alternative definition of $T_K$ which ensures proper scaling. In the last study presented in this thesis we calculate the Fermi-liquid coefficients for fully screened multi-channel Kondo models. For temperatures below $T_K$, these models show Fermi-liquid behavior, and the impurity density of states and certain quantities which depend on it, like resistivity, show quadratic dependencies on parameters like temperature or magnetic field, described by the Fermi-liquid coefficients. We calculate these coefficients both analytically and numerically.