A time-reversal invariant topological insulator is defined by its topological magnetoelectric response that is robust against disorder. The response formula, defined on a Brillouin torus, defines a $mathbb{Z}_2$ invariant and classifies the topological phase. However, in the presence of disorder or the magnetic field, the notion of Brillouin torus is destroyed and the response formula is no longer well-defined. This has been a challenging open problem, and it is essental in defining a topological insulator. This thesis proposes a topological response theory that is free from this fundamental deficiency. We derived the magnetoelectric response formula in position space for a generic three dimensional model under disorder and finite magnetic field. For time-reversal invariant systems, we connected the result to the 2nd Chern number in Noncommutative Geometry. We developed the noncommutative theory of Chern numbers and showed that the quantization of the magnetoelectric response is robust against disorder. Numerical studies on serveral disodered topological models in 1D and 3D are presented.
Subject (authority = RUETD)
Topic
Physics and Astronomy
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TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
Identifier
ETD_5034
PhysicalDescription
Form (authority = gmd)
electronic resource
InternetMediaType
application/pdf
InternetMediaType
text/xml
Extent
xv, 117 p. : ill.
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
Note (type = statement of responsibility)
by Wing Fung Leung
Subject (authority = ETD-LCSH)
Topic
Topological spaces
Subject (authority = ETD-LCSH)
Topic
Noncommutative differential geometry
RelatedItem (type = host)
TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier (type = local)
rucore19991600001
Location
PhysicalLocation (authority = marcorg); (displayLabel = Rutgers, The State University of New Jersey)
Rutgers University. Graduate School - New Brunswick
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License
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Author Agreement License
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I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.