Optical and transport properties of quantum impurity models - an NRG study of generic models and real physical systems

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.