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@PHDTHESIS{Weber:1003679,
author = {Weber, Clara Stephanie},
othercontributors = {Kennes, Dante Marvin and Schoeller, Herbert},
title = {{R}ealization of topological and unconventional
superconducting behavior in low-dimensional quantum
many-body systems},
school = {RWTH Aachen University},
type = {Dissertation},
address = {Aachen},
publisher = {RWTH Aachen University},
reportid = {RWTH-2025-01206},
pages = {1 Online-Ressource : Illustrationen},
year = {2024},
note = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
University 2025; Dissertation, RWTH Aachen University, 2024},
abstract = {In this thesis, emergent phenomena in low-dimensional (one
or two-dimensional) systems and possible mechanisms behind
them are investigated. Here, we focus on topological
properties, as well as unconventional superconductivity.
Following the introduction of the methods and formalisms
used in this thesis, which are exact diagonalization,
density matrix renormalization group, Green's functions and
generalized Bardeen-Cooper-Schrieffer theory, multiple
physical systems with exotic properties are investigated.
First, we study a subclass of second-order topological
insulators in two dimensions. The chosen subclass is
supersymmetric for an applied Aharanov-Bohm flux of half a
flux quantum through the system's center. The present
supersymmetry leads to a fully two-fold degenerate spectrum
and is, in combination with a chiral symmetry, responsible
for the protection of zero-dimensional topological bound
states at zero energy. At the example of the
Bernevig-Hughes-Zhang model, the spectrum as well as the
zero energy bound states are examined in great detail on a
Corbino disk. After the investigation of this
non-interacting topological system, we concentrate on an
interacting system and study superconductors with multiple
competing orders on the level of mean-field approximations.
Here, we examine under which conditions a subleading order
can be metastable. Only if the subleading order is
metastable, it can be targeted by employing a light pulse.
Thereby, under certain conditions, a conventional
superconductor can be driven into an unconventional
superconductor via light switching. Interestingly, we
observe that the phase difference between the multiple
orders can be crucial for the question of metastability.
Moreover, we find that real valuead pairing (such as
$p_{x,y}$) is in general unstable, while topological chiral
instabilities (e.g. $p_{x}\!+\!ip_y$) can be subleading
metastable orders. Hereafter, a second mechanism leading to
unconventional superconductivity, based on strong electronic
couplings, is investigated. Here, we study a weakly- and a
strongly-interacting layer coupled and combined into a
hetero bilayer structure. This leads to an effective
attractive interaction yielding Cooper pairs mostly present
in the nearly-metallic layer. In the strong coupling regime,
the appearance of electronic pairs is explained using a
single rung and the superconducting behavior is found to be
intertwined with magnetic ordering. Using numerical methods,
we investigate both, the superconducting and the magnetic
ordering which continue to exist beyond the strong coupling
regime. Remarkably, some parts of the phase diagram do not
show uniform pairing but instead a pair density wave is
formed here. Finally, possible systems that can possess the
needed strong correlations are discussed in more detail.
Here, we focus on systems with a partially filled flat band
but disregard possible electronic correlations. We study the
behavior of the Ruderman-Kittel-Kasuya-Yosida interaction,
which describes indirect couplings of impurity spins, in one
dimension. The Ruderman-Kittel-Kasuya-Yosida interaction is
usually calculated using a perturbative expression. This
approach cannot be employed in flat band systems due to the
vanishing band width, making an exact treatment necessary.
Indeed, we find that the standard approach does not cover
the results if at least one of the impurities is directly
coupled to the eigenstates of the flat band. Additionally,
the decay of the Ruderman-Kittel-Kasuya-Yosida coupling in
real space depends on the band structure of the system. In
systems with a flat band isolated by a band gap, an
exponential decay occurs, while systems, where other bands
cross the flat band, have a Ruderman-Kittel-Kasuya-Yosida
interaction with an algebraic powerlaw decay (in the limit
of large distances).},
cin = {135320 ; 135310 / 130000},
ddc = {530},
cid = {$I:(DE-82)135320_20180927$ / $I:(DE-82)130000_20140620$},
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-2025-01206},
url = {https://publications.rwth-aachen.de/record/1003679},
}
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