Topological electronic bands in crystalline solids
Topology is now securely established as a means to explore and classify electronic states in crystalline solids. This review provides a gentle but firm introduction to topological electronic band structure suitable for new researchers in the field. I begin by outlining the relevant concepts from top...
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| Format: | Journal article |
| Language: | English |
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Taylor and Francis
2023
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| _version_ | 1826314677505753088 |
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| author | Boothroyd, AT |
| author_facet | Boothroyd, AT |
| author_sort | Boothroyd, AT |
| collection | OXFORD |
| description | Topology is now securely established as a means to explore and classify electronic states in crystalline solids. This review provides a gentle but firm introduction to topological electronic band structure suitable for new researchers in the field. I begin by outlining the relevant concepts from topology, then give a summary of the theory of non-interacting electrons in periodic potentials. Next, I explain the concepts of the Berry phase and Berry curvature, and derive key formulae. The remainder of the article deals with how these ideas are applied to classify crystalline solids according to the topology of the electronic states, and the implications for observable properties. Among the topics covered are the role of symmetry in determining band degeneracies in momentum space, the Chern number and 𝒵2 topological invariants, surface electronic states, two- and three-dimensional topological insulators, and Weyl and Dirac semimetals |
| first_indexed | 2024-03-07T08:10:38Z |
| format | Journal article |
| id | oxford-uuid:1e4f0a1d-2a3f-4ace-90e8-fbf55e59055e |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-12-09T03:09:03Z |
| publishDate | 2023 |
| publisher | Taylor and Francis |
| record_format | dspace |
| spelling | oxford-uuid:1e4f0a1d-2a3f-4ace-90e8-fbf55e59055e2024-10-07T11:45:07ZTopological electronic bands in crystalline solidsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:1e4f0a1d-2a3f-4ace-90e8-fbf55e59055eEnglishSymplectic ElementsTaylor and Francis2023Boothroyd, ATTopology is now securely established as a means to explore and classify electronic states in crystalline solids. This review provides a gentle but firm introduction to topological electronic band structure suitable for new researchers in the field. I begin by outlining the relevant concepts from topology, then give a summary of the theory of non-interacting electrons in periodic potentials. Next, I explain the concepts of the Berry phase and Berry curvature, and derive key formulae. The remainder of the article deals with how these ideas are applied to classify crystalline solids according to the topology of the electronic states, and the implications for observable properties. Among the topics covered are the role of symmetry in determining band degeneracies in momentum space, the Chern number and 𝒵2 topological invariants, surface electronic states, two- and three-dimensional topological insulators, and Weyl and Dirac semimetals |
| spellingShingle | Boothroyd, AT Topological electronic bands in crystalline solids |
| title | Topological electronic bands in crystalline solids |
| title_full | Topological electronic bands in crystalline solids |
| title_fullStr | Topological electronic bands in crystalline solids |
| title_full_unstemmed | Topological electronic bands in crystalline solids |
| title_short | Topological electronic bands in crystalline solids |
| title_sort | topological electronic bands in crystalline solids |
| work_keys_str_mv | AT boothroydat topologicalelectronicbandsincrystallinesolids |