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postgraduate thesis: Theoretical studies on disordered topological semi-metals

TitleTheoretical studies on disordered topological semi-metals
Authors
Advisors
Advisor(s):Wang, Z
Issue Date2017
PublisherThe University of Hong Kong (Pokfulam, Hong Kong)
Citation
Huang, X. [黃先嘉]. (2017). Theoretical studies on disordered topological semi-metals. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR.
AbstractDoubtlessly, topological insulators and superconductors as well as graphene are two most exciting and attracting fields in condensed matter physics in the most recent decade. In consequence, as the combination of these two, topological semi-metals, which on the one hand show unconventional band structures similarly to graphene, on the other also topologically non-trivial, have gained mass attention in the past few years. For instance, Weyl semi-metals, the most well-known example of two-dimensional topological semi-metals, have shown not only rich physics but many novel observable properties. And it is noteworthy that the unconventional transport properties of topological semi-metals are robust against disorders, and the stabilities are ensured by the topological non-triviality in a manner which is exactly the same as how those surface states are protected by topology in the case of topological insulators and superconductors. In this thesis, general theories of topological semi-metals in both even-dimensional chiral-symmetry-preserving and odd-dimensional chiral-symmetry-breaking cases are going to be formulated. To be specific, in presence of disorder, an anisotropic topological term would emerge in both the action of non-linear sigma model and effective response action subjected to an external U(1) gauge field. In the language of both non-linear sigma model and gauge theory, the two types of anisotropic topological terms of topological semi-metals in any dimensions are going to be derived and discussed. In addition, the relationship between topological semi-metals and topological insulators and superconductors or fermions in field theory is going to be revealed as well. In other words, the topological semi-metals are going to be included in the great family of topological quantum matter with symmetries. This thesis is organised as follow: Chapter 1 gives a brief introduction of backgrounds of this topic and introduces the well-established classification of topological quantum matter with symmetries and the mathematical essence behind as well. In Chapter 2, the theory of disorder and non-linear sigma model is briefly introduced, and anisotropic topological theta-terms of topological semi-metals in odd and even dimensions are obtained respectively. In chapter 3, similarly, for topological semi-metals coupled to an external U(1) gauge field in odd and even dimensions, the anisotropic topological Chern-Simons term and Chern character term are developed respectively. Finally, we note that the stabilities against disorders of the electromagnetic responses given by anisotropic topological terms in gauge theory are ensured by the anisotropic topological terms in the action of non-linear sigma model.
DegreeDoctor of Philosophy
SubjectSemimetals
Dept/ProgramPhysics
Persistent Identifierhttp://hdl.handle.net/10722/255058

 

DC FieldValueLanguage
dc.contributor.advisorWang, Z-
dc.contributor.authorHuang, Xianjia-
dc.contributor.author黃先嘉-
dc.date.accessioned2018-06-21T03:42:05Z-
dc.date.available2018-06-21T03:42:05Z-
dc.date.issued2017-
dc.identifier.citationHuang, X. [黃先嘉]. (2017). Theoretical studies on disordered topological semi-metals. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR.-
dc.identifier.urihttp://hdl.handle.net/10722/255058-
dc.description.abstractDoubtlessly, topological insulators and superconductors as well as graphene are two most exciting and attracting fields in condensed matter physics in the most recent decade. In consequence, as the combination of these two, topological semi-metals, which on the one hand show unconventional band structures similarly to graphene, on the other also topologically non-trivial, have gained mass attention in the past few years. For instance, Weyl semi-metals, the most well-known example of two-dimensional topological semi-metals, have shown not only rich physics but many novel observable properties. And it is noteworthy that the unconventional transport properties of topological semi-metals are robust against disorders, and the stabilities are ensured by the topological non-triviality in a manner which is exactly the same as how those surface states are protected by topology in the case of topological insulators and superconductors. In this thesis, general theories of topological semi-metals in both even-dimensional chiral-symmetry-preserving and odd-dimensional chiral-symmetry-breaking cases are going to be formulated. To be specific, in presence of disorder, an anisotropic topological term would emerge in both the action of non-linear sigma model and effective response action subjected to an external U(1) gauge field. In the language of both non-linear sigma model and gauge theory, the two types of anisotropic topological terms of topological semi-metals in any dimensions are going to be derived and discussed. In addition, the relationship between topological semi-metals and topological insulators and superconductors or fermions in field theory is going to be revealed as well. In other words, the topological semi-metals are going to be included in the great family of topological quantum matter with symmetries. This thesis is organised as follow: Chapter 1 gives a brief introduction of backgrounds of this topic and introduces the well-established classification of topological quantum matter with symmetries and the mathematical essence behind as well. In Chapter 2, the theory of disorder and non-linear sigma model is briefly introduced, and anisotropic topological theta-terms of topological semi-metals in odd and even dimensions are obtained respectively. In chapter 3, similarly, for topological semi-metals coupled to an external U(1) gauge field in odd and even dimensions, the anisotropic topological Chern-Simons term and Chern character term are developed respectively. Finally, we note that the stabilities against disorders of the electromagnetic responses given by anisotropic topological terms in gauge theory are ensured by the anisotropic topological terms in the action of non-linear sigma model.-
dc.languageeng-
dc.publisherThe University of Hong Kong (Pokfulam, Hong Kong)-
dc.relation.ispartofHKU Theses Online (HKUTO)-
dc.rightsThe author retains all proprietary rights, (such as patent rights) and the right to use in future works.-
dc.rightsThis work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.-
dc.subject.lcshSemimetals-
dc.titleTheoretical studies on disordered topological semi-metals-
dc.typePG_Thesis-
dc.description.thesisnameDoctor of Philosophy-
dc.description.thesislevelDoctoral-
dc.description.thesisdisciplinePhysics-
dc.description.naturepublished_or_final_version-
dc.identifier.doi10.5353/th_991044014359203414-
dc.date.hkucongregation2018-
dc.identifier.mmsid991044014359203414-

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