{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/97306"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/97306","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Examining mean-field approximations and Bogoliubov-de Gennes (BdG) equations for topological quantum computing - some considerations on the conceptual basis of Majorana zero modes in p+ip superconductors","abstract":"The current theoretical framework for studying Majorana zero modes (MZM) in superconductors and its application for topological quantum computing is based on mean-field approximations and is derived from solutions to BdG equations. In this framework, particle number conservation is broken and non-interacting fermion Hamiltonian is used to describe physics of interest. We argue that these features in the current framework may make it insufficient for studying topological properties of MZM pertinent to quantum computing. After reviewing the current theory with an emphasis on its potential problems, we investigate physics beyond the BdG equations in a toy model and find evidence for the non-trivial role of particle number conservation in Berry phase of transporting a bound quasiparticle around a vortex in a s-wave superconductor. We then study the effect of particle number conservation and superconducting condensate on braiding MZM in vortices in chiral p-wave superconductors and find that they may have non-negligible effect on properties of MZM, suggesting the need for further study on the theoretical basis of this intriguing subject.","abstract_html":"The current theoretical framework for studying Majorana zero modes (MZM) in superconductors and its application for topological quantum computing is based on mean-field approximations and is derived from solutions to BdG equations. In this framework, particle number conservation is broken and non-interacting fermion Hamiltonian is used to describe physics of interest. We argue that these features in the current framework may make it insufficient for studying topological properties of MZM pertinent to quantum computing. After reviewing the current theory with an emphasis on its potential problems, we investigate physics beyond the BdG equations in a toy model and find evidence for the non-trivial role of particle number conservation in Berry phase of transporting a bound quasiparticle around a vortex in a s-wave superconductor. We then study the effect of particle number conservation and superconducting condensate on braiding MZM in vortices in chiral p-wave superconductors and find that they may have non-negligible effect on properties of MZM, suggesting the need for further study on the theoretical basis of this intriguing subject.","abstract_has_math":false,"creators":["Lin, Yiruo"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Leggett, Anthony J.","Stone, Michael","Eckstein, James N.","Kwiat, Paul G."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017-08-10T19:14:44Z","date_published":"2017-08-10T19:14:44Z","updated_at":"2026-07-22T22:24:32Z","subjects":["Mean-field approximations","Bogoliubov-de Gennes (BdG) equations","Particle number conservation","Majorana zero modes","P+ip superconductors","Topological quantum computing"],"languages":["en"],"rights":["Copyright 2017 Yiruo Lin"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/97306","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Leggett, Anthony J.","Stone, Michael","Eckstein, James N.","Kwiat, Paul G."]},{"key":"dc:creator","label":"Author","values":["Lin, Yiruo"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2017-08-10T19:14:44Z","2017-04-06","2017-05"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Physics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mean-field approximations","Bogoliubov-de Gennes (BdG) equations","Particle number conservation","Majorana zero modes","P+ip superconductors","Topological quantum computing"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2017 Yiruo Lin"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/97306"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The current theoretical framework for studying Majorana zero modes (MZM) in superconductors and its application for topological quantum computing is based on mean-field approximations and is derived from solutions to BdG equations. In this framework, particle number conservation is broken and non-interacting fermion Hamiltonian is used to describe physics of interest. We argue that these features in the current framework may make it insufficient for studying topological properties of MZM pertinent to quantum computing. After reviewing the current theory with an emphasis on its potential problems, we investigate physics beyond the BdG equations in a toy model and find evidence for the non-trivial role of particle number conservation in Berry phase of transporting a bound quasiparticle around a vortex in a s-wave superconductor. We then study the effect of particle number conservation and superconducting condensate on braiding MZM in vortices in chiral p-wave superconductors and find that they may have non-negligible effect on properties of MZM, suggesting the need for further study on the theoretical basis of this intriguing subject.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2017-08-10 without embargo terms","The student, Yiruo Lin, accepted the attached license on 2017-04-05 at 14:48.","The student, Yiruo Lin, submitted this Dissertation for approval on 2017-04-05 at 15:06.","This Dissertation was approved for publication on 2017-04-06 at 10:44.","DSpace SAF Submission Ingestion Package generated from Vireo submission #10654 on 2017-08-10 at 13:38:48","Made available in DSpace on 2017-08-10T19:14:44Z (GMT). No. of bitstreams: 2 LIN-DISSERTATION-2017.pdf: 3275444 bytes, checksum: f167c8719ecc91b81803700a2dddbdf7 (MD5) LICENSE.txt: 4206 bytes, checksum: be6ab8259eeb82708309e48368fe6269 (MD5) Previous issue date: 2017-04-06"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Examining mean-field approximations and Bogoliubov-de Gennes (BdG) equations for topological quantum computing - some considerations on the conceptual basis of Majorana zero modes in p+ip superconductors"]}]}],"canonical_facts":{"dc:contributor":["Leggett, Anthony J.","Stone, Michael","Eckstein, James N.","Kwiat, Paul G."],"dc:creator":["Lin, Yiruo"],"dc:date":["2017-08-10T19:14:44Z","2017-04-06","2017-05"],"dc:description":["The current theoretical framework for studying Majorana zero modes (MZM) in superconductors and its application for topological quantum computing is based on mean-field approximations and is derived from solutions to BdG equations. In this framework, particle number conservation is broken and non-interacting fermion Hamiltonian is used to describe physics of interest. We argue that these features in the current framework may make it insufficient for studying topological properties of MZM pertinent to quantum computing. After reviewing the current theory with an emphasis on its potential problems, we investigate physics beyond the BdG equations in a toy model and find evidence for the non-trivial role of particle number conservation in Berry phase of transporting a bound quasiparticle around a vortex in a s-wave superconductor. We then study the effect of particle number conservation and superconducting condensate on braiding MZM in vortices in chiral p-wave superconductors and find that they may have non-negligible effect on properties of MZM, suggesting the need for further study on the theoretical basis of this intriguing subject.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2017-08-10 without embargo terms","The student, Yiruo Lin, accepted the attached license on 2017-04-05 at 14:48.","The student, Yiruo Lin, submitted this Dissertation for approval on 2017-04-05 at 15:06.","This Dissertation was approved for publication on 2017-04-06 at 10:44.","DSpace SAF Submission Ingestion Package generated from Vireo submission #10654 on 2017-08-10 at 13:38:48","Made available in DSpace on 2017-08-10T19:14:44Z (GMT). No. of bitstreams: 2 LIN-DISSERTATION-2017.pdf: 3275444 bytes, checksum: f167c8719ecc91b81803700a2dddbdf7 (MD5) LICENSE.txt: 4206 bytes, checksum: be6ab8259eeb82708309e48368fe6269 (MD5) Previous issue date: 2017-04-06"],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/97306"],"dc:language":["en"],"dc:rights":["Copyright 2017 Yiruo Lin"],"dc:subject":["Mean-field approximations","Bogoliubov-de Gennes (BdG) equations","Particle number conservation","Majorana zero modes","P+ip superconductors","Topological quantum computing"],"dc:title":["Examining mean-field approximations and Bogoliubov-de Gennes (BdG) equations for topological quantum computing - some considerations on the conceptual basis of Majorana zero modes in p+ip superconductors"],"dc:type":["text"],"thesis:degree_discipline":["Physics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:32Z"}