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Emergent topological phenomena in low-dimensional systems induced by gauge potentials

dc.contributor.authorWinblad, Aidan, author
dc.contributor.authorChen, Hua, advisor
dc.contributor.authorEykholt, Richard, committee member
dc.contributor.authorGelfand, Martin, committee member
dc.contributor.authorPinaud, Olivier, committee member
dc.date.accessioned2025-06-02T15:21:32Z
dc.date.available2025-06-02T15:21:32Z
dc.date.issued2025
dc.description.abstractIn this dissertation we discuss how gauge potentials can be used as a key ingredient for inducing topological phase transitions in condensed matter systems, such as conductors, insulators, and superconductors. The first chapter covers some important background physics: Maxwell's equations, gauge invariance, minimal coupling, and Peierls phase, etc. It then presents a review of how one can realize Majorana fermions (MFs) in superconductors and their importance to topological quantum computing. In the end of chapter 1, we give an overview of the basics of Landau levels (LLs) and their relation to the Chern number. Chapter 2 presents a theoretical proposal for inducing topological phase transitions that allow for MFs to be hosted and rotated along the corners of a hollow equilateral triangle, which can serve as a basic building block for topological quantum logic gates. This provides a potential new avenue for achieving a topological quantum computation where a network of interconnected triangular islands allows for braiding of MFs. In chapter 3 we show using Floquet theory and high-frequency expansion, that oblique incident, circularly polarized light can give rise to spectral features analogous to Landau levels in the quantum Hall effect (QHE), where the effective magnetic field is related to the electric field of the laser light. Outside of having the electric field as a useful parameter for achieving a QHE device, this finding enables us to explore non-equilibrium systems exhibiting topological phenomena in the absence of spatial periodicity. Chapter 4 concludes and discusses further implications of the work in this dissertation.
dc.format.mediumborn digital
dc.format.mediumdoctoral dissertations
dc.identifierWinblad_colostate_0053A_18974.pdf
dc.identifier.urihttps://hdl.handle.net/10217/241098
dc.languageEnglish
dc.language.isoeng
dc.publisherColorado State University. Libraries
dc.relation.ispartof2020-
dc.rightsCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.
dc.subjectgauge potentials
dc.subjectquantum Hall effect
dc.subjectsuperconductors
dc.subjectmajorana fermions
dc.subjectFloquet
dc.subjectquantum topological computing
dc.titleEmergent topological phenomena in low-dimensional systems induced by gauge potentials
dc.typeText
dcterms.rights.dplaThis Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
thesis.degree.disciplinePhysics
thesis.degree.grantorColorado State University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy (Ph.D.)

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