Over the last decades, both band topology and Anderson transitions, as well as their interplay, have been well understood in the context of time-independent energy-conserved systems. This switches the research focus in this field from theoretical descriptions to experimental designs, realizations, and engineering. In such a background, time-dependent perturbations and coupling between quantum systems and environments become the main concern.
Along this route, this dissertation first studies the properties of a Chern insulator, one of the simplest topological systems, under time-periodic disorder. We reveal that in certain cases disorder fully localizes the bulk, but surprisingly has a positive effect on the edge, propagating edge states exist throughout the full spectrum. Along this direction, we further explore disorder effects in a network model constructed by arrays of unitary scattering matrices. Here, we go beyond previous works and show that also the shape of network (lattice symmetries) is important. It will result in a new type of topological phase, known as a higher-order topological phase, in which the topological states of a d-dimensional system have a dimension less than (d − 1). Afterwards, we focus on a network model with gain and loss, which breaks energy conservation. Here, we find the system now exhibits a 'supermetal' behavior that surpasses the conventional ballistic transport for perfect metals. At the end of this dissertation, we perform a study on the non-Hermitian defect in time-periodic systems. Our study shows that a boundary defect, due to its non-Hermiticity, can stop the propagation of chiral edge states, which should otherwise be the most robust manifestations of topology in quantum systems.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:85873 |
| Date | 08 June 2023 |
| Creators | Liu, Hui |
| Contributors | van den Brink, Jeroen, Fulga, Ion Cosma, Asbóth, János K., Technische Universität Dresden |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, doc-type:doctoralThesis, info:eu-repo/semantics/doctoralThesis, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
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