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%0 Thesis
%A Weber, Clara Stephanie
%T Realization of topological and unconventional superconducting behavior in low-dimensional quantum many-body systems
%I RWTH Aachen University
%V Dissertation
%C Aachen
%M RWTH-2025-01206
%P 1 Online-Ressource : Illustrationen
%D 2024
%Z Veröffentlicht auf dem Publikationsserver der RWTH Aachen University 2025
%Z Dissertation, RWTH Aachen University, 2024
%X 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<sub>x,y</sub>) is in general unstable, while topological chiral instabilities (e.g. p<sub>x</sub>+ip<sub>y</sub>) 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).
%F PUB:(DE-HGF)11
%9 Dissertation / PhD Thesis
%R 10.18154/RWTH-2025-01206
%U https://publications.rwth-aachen.de/record/1003679