{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/44335"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/44335","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"The classification of topological insulators and superconductors for non-spatial and spatial symmetries","abstract":"We study a topological classification of insulators and superconductors in the presence of non-spatial discrete symmetries in the Altland-Zirnbauer classification and spatial symmetries in any spatial dimension. We provide a unified method, the construction of bulk Dirac Hamiltonians in minimal matrix dimension, to classify topological phases. Using this method, we first reproduce the classification of non-spatial symmetric topological insulators and superconductors in the Altland-Zirnbauer symmetry classes. Such non-trivial topological insulators and superconductors possess protected gapless modes in each boundary. Furthermore, we extend the classification to spatial symmetric systems, such as reflection symmetry. When a specific boundary that does not break system's symmetries is introduced in these non-trivial topological systems, gapless modes are present at this boundary.","abstract_html":"We study a topological classification of insulators and superconductors in the presence of non-spatial discrete symmetries in the Altland-Zirnbauer classification and spatial symmetries in any spatial dimension. We provide a unified method, the construction of bulk Dirac Hamiltonians in minimal matrix dimension, to classify topological phases. Using this method, we first reproduce the classification of non-spatial symmetric topological insulators and superconductors in the Altland-Zirnbauer symmetry classes. Such non-trivial topological insulators and superconductors possess protected gapless modes in each boundary. Furthermore, we extend the classification to spatial symmetric systems, such as reflection symmetry. When a specific boundary that does not break system's symmetries is introduced in these non-trivial topological systems, gapless modes are present at this boundary.","abstract_has_math":false,"creators":["Chiu, Ching-Kai"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Stone, Michael","Ryu, Shinsei","Chiang, Tai-Chang","Gilbert, Matthew J.","Cooper, S. 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We provide a unified method, the construction of bulk Dirac Hamiltonians in minimal matrix dimension, to classify topological phases. Using this method, we first reproduce the classification of non-spatial symmetric topological insulators and superconductors in the Altland-Zirnbauer symmetry classes. Such non-trivial topological insulators and superconductors possess protected gapless modes in each boundary. Furthermore, we extend the classification to spatial symmetric systems, such as reflection symmetry. When a specific boundary that does not break system's symmetries is introduced in these non-trivial topological systems, gapless modes are present at this boundary.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2013-04-15T21:14:02Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 2 bundle_Chiu_Ching-Kai.zip: 1365703 bytes, checksum: 7f5882de50e0567fb484fc129c05b867 (MD5) Chiu_Ching-Kai.pdf: 2203132 bytes, checksum: 53d512b68edf11ce81a650c58d5e2902 (MD5)","Made available in DSpace on 2013-05-24T22:08:12Z (GMT). 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We provide a unified method, the construction of bulk Dirac Hamiltonians in minimal matrix dimension, to classify topological phases. Using this method, we first reproduce the classification of non-spatial symmetric topological insulators and superconductors in the Altland-Zirnbauer symmetry classes. Such non-trivial topological insulators and superconductors possess protected gapless modes in each boundary. Furthermore, we extend the classification to spatial symmetric systems, such as reflection symmetry. 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