File Download
Supplementary

postgraduate thesis: Theoretical studies of topological DIII-class chains and Weyl semimetals / y Ting Mao, MSci. Nanjing University

TitleTheoretical studies of topological DIII-class chains and Weyl semimetals / y Ting Mao, MSci. Nanjing University
Authors
Issue Date2015
PublisherThe University of Hong Kong (Pokfulam, Hong Kong)
Citation
Mao, T. [毛汀]. (2015). Theoretical studies of topological DIII-class chains and Weyl semimetals. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b5543997
AbstractTopological insulators and superconductors, which are featured by not only the topological characteristics of their gapped bulk band structure but also the special edge or surface states, have attracted great attention in the past few years. A complete classification of topological insulators and superconductors in terms of symmetry and spatial dimension has been established, while the application of their surface states remains a challenge. The gapless phases which have topologically stable Fermi surfaces could also exhibit peculiar surface states and topological transport phenomena in the bulk. In this thesis, the topological DIII-classs superconducting chains and the application of its Majorana edge states are studied. On the other hand, Weyl semimetals, as the representative example of topological gapless phases, and its exotic transport phenomena are also investigated. Majorana edge states have been a focus of condensed matter research for their potential applications in topological quantum computation, which appear in the topological DIII-class superconducting chains protected by both the particle-hole and time reversal symmetries. We utilize two charge-qubit arrays to explicitly simulate one type of DIII-class superconducting chains and the universal quantum operations performed on the Majorana edge states. It is shown that combined with one braiding operation, universal single-qubit operations on a Majorana-based qubit can be implemented by a controllable inductive coupling between two charge qubits at the ends of the arrays. It is further shown that in a similar way, a controlled-NOT gate for two topological qubits can be simulated in four charge-qubit arrays. Although the current scheme may not truly realize topological quantum operations, we elaborate that the operations in charge-qubit arrays are indeed robust against certain local perturbations. Weyl semimetals possess nontrivial Fermi surface topology in that the pair of Weyl points with opposite topological charges is separated from each other in momentum space. The physical manifestations of this Fermi surface topology are protected surface states and exotic transport phenomena including the anomalous Hall effect as well as the chiral magnetic effect. By studying the path integral measure under the chiral transformation, it is shown that these transport phenomena can be described by the chiral anomaly which appears when the chiral Weyl fermion couples to the topologically nontrivial gauge field. The case of the gauge anomaly for the Weyl fermion coupled to a non-Abelian gauge field is also discussed.
DegreeDoctor of Philosophy
SubjectSemimetals
Topological dynamics
Dept/ProgramPhysics
Persistent Identifierhttp://hdl.handle.net/10722/212613

 

DC FieldValueLanguage
dc.contributor.authorMao, Ting-
dc.contributor.author毛汀-
dc.date.accessioned2015-07-23T23:10:49Z-
dc.date.available2015-07-23T23:10:49Z-
dc.date.issued2015-
dc.identifier.citationMao, T. [毛汀]. (2015). Theoretical studies of topological DIII-class chains and Weyl semimetals. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b5543997-
dc.identifier.urihttp://hdl.handle.net/10722/212613-
dc.description.abstractTopological insulators and superconductors, which are featured by not only the topological characteristics of their gapped bulk band structure but also the special edge or surface states, have attracted great attention in the past few years. A complete classification of topological insulators and superconductors in terms of symmetry and spatial dimension has been established, while the application of their surface states remains a challenge. The gapless phases which have topologically stable Fermi surfaces could also exhibit peculiar surface states and topological transport phenomena in the bulk. In this thesis, the topological DIII-classs superconducting chains and the application of its Majorana edge states are studied. On the other hand, Weyl semimetals, as the representative example of topological gapless phases, and its exotic transport phenomena are also investigated. Majorana edge states have been a focus of condensed matter research for their potential applications in topological quantum computation, which appear in the topological DIII-class superconducting chains protected by both the particle-hole and time reversal symmetries. We utilize two charge-qubit arrays to explicitly simulate one type of DIII-class superconducting chains and the universal quantum operations performed on the Majorana edge states. It is shown that combined with one braiding operation, universal single-qubit operations on a Majorana-based qubit can be implemented by a controllable inductive coupling between two charge qubits at the ends of the arrays. It is further shown that in a similar way, a controlled-NOT gate for two topological qubits can be simulated in four charge-qubit arrays. Although the current scheme may not truly realize topological quantum operations, we elaborate that the operations in charge-qubit arrays are indeed robust against certain local perturbations. Weyl semimetals possess nontrivial Fermi surface topology in that the pair of Weyl points with opposite topological charges is separated from each other in momentum space. The physical manifestations of this Fermi surface topology are protected surface states and exotic transport phenomena including the anomalous Hall effect as well as the chiral magnetic effect. By studying the path integral measure under the chiral transformation, it is shown that these transport phenomena can be described by the chiral anomaly which appears when the chiral Weyl fermion couples to the topologically nontrivial gauge field. The case of the gauge anomaly for the Weyl fermion coupled to a non-Abelian gauge field is also discussed.-
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.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subject.lcshSemimetals-
dc.subject.lcshTopological dynamics-
dc.titleTheoretical studies of topological DIII-class chains and Weyl semimetals / y Ting Mao, MSci. Nanjing University-
dc.typePG_Thesis-
dc.identifier.hkulb5543997-
dc.description.thesisnameDoctor of Philosophy-
dc.description.thesislevelDoctoral-
dc.description.thesisdisciplinePhysics-
dc.description.naturepublished_or_final_version-

Export via OAI-PMH Interface in XML Formats


OR


Export to Other Non-XML Formats