Numerical Renormalization Group studies of Correlation effects in Phase Coherent Transport through Quantum Dots

This thesis contributes to the field of transport through quantum
dots. These devices allow for a controlled study of quantum
transport and fundamental physical effects, like the Kondo effect.
In this thesis we will focus on dots that are well described by
generalized Anderson impurity models, where the discrete levels of
the quantum dot are tunnel-coupled to fermionic reservoirs. The
model parameters, like level energy and width, can be tuned in
experiments. Therefore these systems constitute a valuable arena
for testing experiment against theory and vice versa. In order to
describe these strongly correlated systems, we employ the numerical
renormalization group method. This allows us to address both
longstanding questions concerning experimental results and new
physical phenomena in these fundamental models. This thesis
consists of three major projects. The first and most extensive one
is concerned with the phase of the transmission amplitude through a
quantum dot. Measurements of many-electron quantum dots with small
level spacing reveal universal phase behaviour, a result not fully
understood for almost 10 years. Recent experiments have seen that,
contrarily, for dots with only a few electrons, i.e. large level
spacing, the phase depends on the mesoscopic dot parameters.
Analyzing a multi-level Anderson model, we show that the generic
feature of the two regimes can be reproduced in the regime of
overlapping levels or well separated levels, respectively. Thereby
the universal character follows from Fano-type antiresonances of
the renormalized single-particle levels. Moderate temperature
supports the universal character. In the mesoscopic regime, we also
investigate the effect of Kondo correlations on the transmission
phase. In a second project we analyze a quantum dot coupled to a
superconducting reservoir. In contrast to previous belief, the
energy resolution of our method is not restricted by the energy
scale of the superconducting gap, leading to new insights into the
method. The high resolution allows us to resolve sharp peaks in the
spectral function that emerge for a certain regime of parameters. A
third project deals with a quantum dot coupled to two independent
channels, a system known to exhibit non-Fermi liquid behaviour. We
investigate the existence of the non-Fermi liquid regime when
driving the system out of the Kondo regime by emptying the dot. We
find that the extent of the non-Fermi liquid regime strongly
depends on the mechanisms that couple impurity and reservoirs but
prevent mixing of the latter.