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@PHDTHESIS{Maurer:973336,
author = {Maurer, Martin Tillmann},
othercontributors = {Schoeller, Herbert and Meden, Volker},
title = {{E}ffects of coherences and topological edge states on
charge fluctuations in quantum dots},
school = {RWTH Aachen University},
type = {Dissertation},
address = {Aachen},
publisher = {RWTH Aachen University},
reportid = {RWTH-2023-10722},
pages = {1 Online-Ressource : Illustrationen, Diagramme},
year = {2023},
note = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
University; Dissertation, RWTH Aachen University, 2023},
abstract = {In this thesis we study effects of coherences and
topological edge states on charge fluctuations in quantum
dots. First, we study coherences in a strongly interacting
quantum dot with $N$ levels weakly tunnel coupled to generic
multichannel metallic reservoirs. We introduce the concepts
of dot and reservoir flavor polarizations to describe the
reduced dot density matrix and the tunnel couplings. In the
regime of coherent sequential tunneling, where the dot-level
detunings are comparable to the coupling strength while both
are much smaller than temperature, we derive
$SU(N)$-invariant representations of the kinetic equation
for the dot density matrix and of the tunneling current in
terms of the flavor polarizations. The kinetic equation for
the dot flavor polarization comprises of three terms
describing flavor accumulation, relaxation, and rotation,
respectively, which gives a physically intuitive picture of
the complex dynamics related to non-equilibrium and
coherences. Besides, our results represent a unified
theoretical framework for the description of multilevel dots
coupled to metallic reservoirs. Furthermore, our study
reveals flavor rotations to lie at the root of off-resonance
negative differential conductances in generic quantum-dot
models. Secondly, we study the effects of topological edge
states on charge fluctuations in a quantum dot tunnel
coupled to the boundary of half-infinite
Su-Schrieffer-Heeger chains. These can exist in a normal or
in a topological phase, hosting an edge state at the
boundary in the latter case. We take a two-step approach. We
begin with the simple model of a single spinless dot level
in the absence of Coulomb interactions. Here we find that
the hybridization and repulsion of the dot and the edge
state bring about characteristic signatures in the dot
spectral function. These are linked to the emergence of a
new broadening scale in the equilibrium dot occupation that
competes with temperature, and to a shift of the resonance
in the non-equilibrium current. Next, we extend the model by
including a second dot orbital and introducing Coulomb
interactions between particles on the dot as well as between
a particle on the dot and a particle in a localized edge
state. We treat this model with a first-order implementation
of the real-time renormalization group, and supplement the
numerical data with an analytical effective model that takes
into account the renormalization of the low-energy sector
due to the strong intra-dot interaction. We identify
renormalization effects in the equilibrium dot occupation
with a lead in its normal phase, and in the non-equilibrium
current. Furthermore, we find fingerprints of an edge state
in the non-equilibrium current, which turn out to depend
qualitatively on the origin of the edge state: An edge state
in the source lead gives rise to the formation of coherent
superpositions of dot states, visible as interference
signatures that depend on the Aharonov-Bohm phase. This
effect is suppressed by the strong intra-dot interaction if
the edge state is in the drain lead, in which case the
central signature is a Coulomb blockade induced by the
dot-edge-state interaction.},
cin = {135110 / 130000},
ddc = {530},
cid = {$I:(DE-82)135110_20140620$ / $I:(DE-82)130000_20140620$},
pnm = {GRK 1995 - GRK 1995: Quantenmechanische
Vielteilchenmethoden in der kondensierten Materie
(240766775)},
pid = {G:(GEPRIS)240766775},
typ = {PUB:(DE-HGF)11},
doi = {10.18154/RWTH-2023-10722},
url = {https://publications.rwth-aachen.de/record/973336},
}
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