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Topological aspects of band theory
Descriptive
TitleInfo
Title
Topological aspects of band theory
Name
(type = personal)
NamePart
(type = family)
Soluyanov
NamePart
(type = given)
Alexey A.
NamePart
(type = date)
1983-
DisplayForm
Alexey Soluyanov
Role
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(authority = RULIB)
author
Name
(type = personal)
NamePart
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Vanderbilt
NamePart
(type = given)
David
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David Vanderbilt
Affiliation
Advisory Committee
Role
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chair
Name
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(type = family)
Kalelkar
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(type = given)
Mohan
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Mohan Kalelkar
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Advisory Committee
Role
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internal member
Name
(type = personal)
NamePart
(type = family)
Rabe
NamePart
(type = given)
Karin
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Karin Rabe
Affiliation
Advisory Committee
Role
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(authority = RULIB)
internal member
Name
(type = personal)
NamePart
(type = family)
Wu
NamePart
(type = given)
Weida
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Weida Wu
Affiliation
Advisory Committee
Role
RoleTerm
(authority = RULIB)
internal member
Name
(type = personal)
NamePart
(type = family)
Mele
NamePart
(type = given)
Eugene
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Eugene Mele
Affiliation
Advisory Committee
Role
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(authority = RULIB)
outside member
Name
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NamePart
Rutgers University
Role
RoleTerm
(authority = RULIB)
degree grantor
Name
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NamePart
Graduate School - New Brunswick
Role
RoleTerm
(authority = RULIB)
school
TypeOfResource
Text
Genre
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theses
OriginInfo
DateCreated
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2012
DateOther
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(type = degree)
2012-10
Place
PlaceTerm
(type = code)
xx
Language
LanguageTerm
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(type = code)
eng
Abstract
(type = abstract)
Band theory has proven to be one of the most successful developments in condensed matter theory. It is the basis of our current understanding of crystalline solids, describing complex electronic behavior in terms of a single quasi-particle that moves in some effective field of the crystal lattice environment and other particles. In recent years topological and geometrical considerations opened a fundamentally new branch of research in band theory. One of the major advances in this field came with the realization that insulating band structures can be classified according to the values of some topological invariants associated with the occupied single-particle states. Insulators that correspond to non-trivial values of these topological invariants realize new states of matter with properties drastically different from those attributed to an ordinary insulator. In this work we address questions that arise in the context of band theory in the presence of topologically non-trivial bands. Part of the thesis is aimed at the actual determination of the presence of non-trivial band topology. We develop a method to distinguish an ordinary insulator from a topological one in the presence of time-reversal symmetry. The method is implemented within the density functional theory framework and is illustrated with applications to real materials in {it ab initio} calculations. Another question considered in this work is that of a real-space representation of topological insulators, and in particular, the construction of Wannier functions -- localized real-space wavefunctions. Wannier functions form one of the most powerful tools in band theory, and it is very important to understand how to implement Wannier function techniques in the presence of topological bands. In some cases bands with non-trivial topology do not allow for the construction of exponentially localized Wannier functions. While previous work has shown that in the presence of time-reversal symmetry such a construction should be possible in principle, it has remained unclear how to do it in practice. We present an explicit construction of a Wannier representation for a particular model of a time-reversal invariant topological insulator. This construction is very different from the one used for ordinary band insulators. We then proceed to develop a procedure that allows for such a construction in the general case, without any reference to a particular model. Our work provides a basis for extending Wannier function techniques to topologically non-trivial band structures.
Subject
(authority = RUETD)
Topic
Physics and Astronomy
RelatedItem
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TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier
(type = RULIB)
ETD
Identifier
ETD_4186
PhysicalDescription
Form
(authority = gmd)
electronic resource
InternetMediaType
application/pdf
InternetMediaType
text/xml
Extent
xiv, 159 p. : ill.
Note
(type = degree)
Ph.D.
Note
(type = bibliography)
Includes bibliographical references
Note
(type = vita)
Includes vita
Note
(type = statement of responsibility)
by Alexey A. Soluyanov
Subject
(authority = ETD-LCSH)
Topic
Energy-band theory of solids
Identifier
(type = hdl)
http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000066990
RelatedItem
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TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
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rucore19991600001
Location
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NjNbRU
Identifier
(type = doi)
doi:10.7282/T3N0159G
Genre
(authority = ExL-Esploro)
ETD doctoral
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Rights
RightsDeclaration
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The author owns the copyright to this work.
RightsHolder
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Name
FamilyName
Soluyanov
GivenName
Alexey
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime
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(qualifier = exact);
(point = start)
2012-08-03 12:29:58
AssociatedEntity
Name
Alexey Soluyanov
Role
Copyright holder
Affiliation
Rutgers University. Graduate School - New Brunswick
AssociatedObject
Type
License
Name
Author Agreement License
Detail
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.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
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