{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/87989"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/87989","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Topological semimetals and nodal superconductors","abstract":"Besides topological band insulators, which have a full bulk gap, there are also gapless phases of matter that belong to the broad class of topological materials, such as topological semimetals and nodal superconductors. We systematically study these gapless topological phases described by the Bloch and Bogoliubov-de Gennes Hamiltonians. We discuss a generalized bulk-boundary correspondence, which relates the topological properties in the bulk of gapless topological phases and the protected zero-energy states at the boundary. We study examples of gapless topological phases, focusing in particular on nodal superconductors, such as nodal noncentrosymmetric superconductors (NCSs). We compute the surface density of states of nodal NCSs and interpret experimental measurements of surface states. In addition, we investigate Majorana vortex-bound states in both nodal and fully gapped NCSs using numerical and analytical methods. We show that different topological properties of the bulk Bogoliubov-quasiparticle wave functions reflect themselves in different types of zero-energy vortex-bound states. In particular, in the case of NCSs with tetragonal point-group symmetry, we find that the stability of these Majorana zero modes is guaranteed by a combination of reflection, time-reversal, and particle-hole symmetries. Finally, by using K-theory arguments and a dimensional reduction procedure from higher-dimensional topological insulators and superconductors, we derive a classification of topologically stable Fermi surfaces in semimetals and nodal lines in superconductors.","abstract_html":"Besides topological band insulators, which have a full bulk gap, there are also gapless phases of matter that belong to the broad class of topological materials, such as topological semimetals and nodal superconductors. We systematically study these gapless topological phases described by the Bloch and Bogoliubov-de Gennes Hamiltonians. We discuss a generalized bulk-boundary correspondence, which relates the topological properties in the bulk of gapless topological phases and the protected zero-energy states at the boundary. We study examples of gapless topological phases, focusing in particular on nodal superconductors, such as nodal noncentrosymmetric superconductors (NCSs). We compute the surface density of states of nodal NCSs and interpret experimental measurements of surface states. In addition, we investigate Majorana vortex-bound states in both nodal and fully gapped NCSs using numerical and analytical methods. We show that different topological properties of the bulk Bogoliubov-quasiparticle wave functions reflect themselves in different types of zero-energy vortex-bound states. In particular, in the case of NCSs with tetragonal point-group symmetry, we find that the stability of these Majorana zero modes is guaranteed by a combination of reflection, time-reversal, and particle-hole symmetries. Finally, by using K-theory arguments and a dimensional reduction procedure from higher-dimensional topological insulators and superconductors, we derive a classification of topologically stable Fermi surfaces in semimetals and nodal lines in superconductors.","abstract_has_math":false,"creators":["Chang, Po-Yao"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Ryu, Shinsei","Hughes, Taylor L.","Mason, Nadya","Cooper, S. Lance"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-29T20:37:56Z","date_published":"2015-09-29T20:37:56Z","updated_at":"2026-07-22T22:26:31Z","subjects":["Topology","Topological semimetals","Nodal superconductors","Entanglement spectrum","Topological insulators","Non-centrosymmetric superconductors","K-theory","Classificaltions"],"languages":["en"],"rights":["Copyright 2015 Po-Yao Chang"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/87989","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Ryu, Shinsei","Hughes, Taylor L.","Mason, Nadya","Cooper, S. 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We systematically study these gapless topological phases described by the Bloch and Bogoliubov-de Gennes Hamiltonians. We discuss a generalized bulk-boundary correspondence, which relates the topological properties in the bulk of gapless topological phases and the protected zero-energy states at the boundary. We study examples of gapless topological phases, focusing in particular on nodal superconductors, such as nodal noncentrosymmetric superconductors (NCSs). We compute the surface density of states of nodal NCSs and interpret experimental measurements of surface states. In addition, we investigate Majorana vortex-bound states in both nodal and fully gapped NCSs using numerical and analytical methods. We show that different topological properties of the bulk Bogoliubov-quasiparticle wave functions reflect themselves in different types of zero-energy vortex-bound states. In particular, in the case of NCSs with tetragonal point-group symmetry, we find that the stability of these Majorana zero modes is guaranteed by a combination of reflection, time-reversal, and particle-hole symmetries. Finally, by using K-theory arguments and a dimensional reduction procedure from higher-dimensional topological insulators and superconductors, we derive a classification of topologically stable Fermi surfaces in semimetals and nodal lines in superconductors.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2015-09-29 without embargo terms","The student, Po-Yao Chang, accepted the attached license on 2015-07-02 at 01:58.","The student, Po-Yao Chang, submitted this Dissertation for approval on 2015-07-02 at 02:21.","This Dissertation was approved for publication on 2015-07-06 at 14:48.","DSpace SAF Submission Ingestion Package generated from Vireo submission #8331 on 2015-09-29 at 13:21:46","Made available in DSpace on 2015-09-29T20:37:56Z (GMT). No. of bitstreams: 2 CHANG-DISSERTATION-2015.pdf: 14317208 bytes, checksum: 2eb96c5ce1a59f995bf8778db36ff861 (MD5) LICENSE.txt: 4209 bytes, checksum: dba7063b39d2b2e97c50dbd429096fb6 (MD5) Previous issue date: 2015-07-06"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Topological semimetals and nodal superconductors"]}]}],"canonical_facts":{"dc:contributor":["Ryu, Shinsei","Hughes, Taylor L.","Mason, Nadya","Cooper, S. Lance"],"dc:creator":["Chang, Po-Yao"],"dc:date":["2015-09-29T20:37:56Z","2015-08","2015-07-06","2015-8"],"dc:description":["Besides topological band insulators, which have a full bulk gap, there are also gapless phases of matter that belong to the broad class of topological materials, such as topological semimetals and nodal superconductors. We systematically study these gapless topological phases described by the Bloch and Bogoliubov-de Gennes Hamiltonians. We discuss a generalized bulk-boundary correspondence, which relates the topological properties in the bulk of gapless topological phases and the protected zero-energy states at the boundary. We study examples of gapless topological phases, focusing in particular on nodal superconductors, such as nodal noncentrosymmetric superconductors (NCSs). We compute the surface density of states of nodal NCSs and interpret experimental measurements of surface states. In addition, we investigate Majorana vortex-bound states in both nodal and fully gapped NCSs using numerical and analytical methods. We show that different topological properties of the bulk Bogoliubov-quasiparticle wave functions reflect themselves in different types of zero-energy vortex-bound states. In particular, in the case of NCSs with tetragonal point-group symmetry, we find that the stability of these Majorana zero modes is guaranteed by a combination of reflection, time-reversal, and particle-hole symmetries. Finally, by using K-theory arguments and a dimensional reduction procedure from higher-dimensional topological insulators and superconductors, we derive a classification of topologically stable Fermi surfaces in semimetals and nodal lines in superconductors.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2015-09-29 without embargo terms","The student, Po-Yao Chang, accepted the attached license on 2015-07-02 at 01:58.","The student, Po-Yao Chang, submitted this Dissertation for approval on 2015-07-02 at 02:21.","This Dissertation was approved for publication on 2015-07-06 at 14:48.","DSpace SAF Submission Ingestion Package generated from Vireo submission #8331 on 2015-09-29 at 13:21:46","Made available in DSpace on 2015-09-29T20:37:56Z (GMT). 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