{"id":"https://openalex.org/W4385767545","doi":"https://doi.org/10.1137/22m1505542","title":"Mathematical Models of Topologically Protected Transport in Twisted Bilayer Graphene","display_name":"Mathematical Models of Topologically Protected Transport in Twisted Bilayer Graphene","publication_year":2023,"publication_date":"2023-08-11","ids":{"openalex":"https://openalex.org/W4385767545","doi":"https://doi.org/10.1137/22m1505542"},"language":"en","primary_location":{"id":"doi:10.1137/22m1505542","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1505542","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Multiscale Modeling &amp; Simulation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://vtechworks.lib.vt.edu/bitstreams/463c1047-ff1a-42e4-af6a-9b5c570f0dd0/download","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047341994","display_name":"Guillaume Bal","orcid":"https://orcid.org/0000-0002-4792-7546"},"institutions":[{"id":"https://openalex.org/I39422238","display_name":"University of Illinois Chicago","ror":"https://ror.org/02mpq6x41","country_code":"US","type":"education","lineage":["https://openalex.org/I39422238"]},{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Guillaume Bal","raw_affiliation_strings":["Departments of Statistics and Mathematics and CCAM, University of Chicago, Chicago, IL 60637 USA"],"raw_orcid":"https://orcid.org/0000-0002-4792-7546","affiliations":[{"raw_affiliation_string":"Departments of Statistics and Mathematics and CCAM, University of Chicago, Chicago, IL 60637 USA","institution_ids":["https://openalex.org/I40347166","https://openalex.org/I39422238"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052216694","display_name":"Paul Cazeaux","orcid":"https://orcid.org/0000-0003-2972-2616"},"institutions":[{"id":"https://openalex.org/I859038795","display_name":"Virginia Tech","ror":"https://ror.org/02smfhw86","country_code":"US","type":"education","lineage":["https://openalex.org/I859038795"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Paul Cazeaux","raw_affiliation_strings":["Department of Mathematics, Virginia Tech, Blacksburg, VA 24060 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Virginia Tech, Blacksburg, VA 24060 USA","institution_ids":["https://openalex.org/I859038795"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027811873","display_name":"Daniel Massatt","orcid":"https://orcid.org/0000-0003-0526-4892"},"institutions":[{"id":"https://openalex.org/I121820613","display_name":"Louisiana State University","ror":"https://ror.org/05ect4e57","country_code":"US","type":"education","lineage":["https://openalex.org/I121820613"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daniel Massatt","raw_affiliation_strings":["Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803 USA"],"raw_orcid":"https://orcid.org/0000-0003-0526-4892","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803 USA","institution_ids":["https://openalex.org/I121820613"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056073918","display_name":"Solomon Quinn","orcid":"https://orcid.org/0009-0003-6127-4224"},"institutions":[{"id":"https://openalex.org/I39422238","display_name":"University of Illinois Chicago","ror":"https://ror.org/02mpq6x41","country_code":"US","type":"education","lineage":["https://openalex.org/I39422238"]},{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Solomon Quinn","raw_affiliation_strings":["Departments of Statistics and Mathematics and CCAM, University of Chicago, Chicago, IL 60637 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departments of Statistics and Mathematics and CCAM, University of Chicago, Chicago, IL 60637 USA","institution_ids":["https://openalex.org/I40347166","https://openalex.org/I39422238"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5047341994"],"corresponding_institution_ids":["https://openalex.org/I39422238","https://openalex.org/I40347166"],"apc_list":null,"apc_paid":null,"fwci":0.9336,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.70361452,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"21","issue":"3","first_page":"1081","last_page":"1121"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10083","display_name":"Graphene research and applications","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10083","display_name":"Graphene research and applications","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10657","display_name":"Topological Materials and Phenomena","score":1.0,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11804","display_name":"Quantum many-body systems","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.541641116142273},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5295829772949219},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.4664117097854614},{"id":"https://openalex.org/keywords/stacking","display_name":"Stacking","score":0.4281831979751587},{"id":"https://openalex.org/keywords/topological-conjugacy","display_name":"Topological conjugacy","score":0.4113249182701111},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.39963269233703613},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3748213052749634},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.32971498370170593},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2324545681476593},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.12602534890174866}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.541641116142273},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5295829772949219},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4664117097854614},{"id":"https://openalex.org/C33347731","wikidata":"https://www.wikidata.org/wiki/Q285210","display_name":"Stacking","level":2,"score":0.4281831979751587},{"id":"https://openalex.org/C165263651","wikidata":"https://www.wikidata.org/wiki/Q2443460","display_name":"Topological conjugacy","level":2,"score":0.4113249182701111},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.39963269233703613},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3748213052749634},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.32971498370170593},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2324545681476593},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.12602534890174866},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C46141821","wikidata":"https://www.wikidata.org/wiki/Q209402","display_name":"Nuclear magnetic resonance","level":1,"score":0.0},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.0},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/22m1505542","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1505542","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Multiscale Modeling &amp; Simulation","raw_type":"journal-article"},{"id":"pmh:oai:vtechworks.lib.vt.edu:10919/117943","is_oa":true,"landing_page_url":"https://hdl.handle.net/10919/117943","pdf_url":"https://vtechworks.lib.vt.edu/bitstreams/463c1047-ff1a-42e4-af6a-9b5c570f0dd0/download","source":{"id":"https://openalex.org/S4306400248","display_name":"VTechWorks (Virginia Tech)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I859038795","host_organization_name":"Virginia Tech","host_organization_lineage":["https://openalex.org/I859038795"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"},{"id":"pmh:oai:repository.lsu.edu:mathematics_pubs-2563","is_oa":true,"landing_page_url":"https://repository.lsu.edu/mathematics_pubs/1561","pdf_url":null,"source":{"id":"https://openalex.org/S4210169993","display_name":"Civil War Book Review","issn_l":"1528-6592","issn":["1528-6592"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310315936","host_organization_name":"Louisiana State University","host_organization_lineage":["https://openalex.org/P4310315936"],"host_organization_lineage_names":["Louisiana State University"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty Publications","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:vtechworks.lib.vt.edu:10919/117943","is_oa":true,"landing_page_url":"https://hdl.handle.net/10919/117943","pdf_url":"https://vtechworks.lib.vt.edu/bitstreams/463c1047-ff1a-42e4-af6a-9b5c570f0dd0/download","source":{"id":"https://openalex.org/S4306400248","display_name":"VTechWorks (Virginia Tech)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I859038795","host_organization_name":"Virginia Tech","host_organization_lineage":["https://openalex.org/I859038795"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","score":0.6899999976158142,"id":"https://metadata.un.org/sdg/11"}],"awards":[{"id":"https://openalex.org/G1930546695","display_name":null,"funder_award_id":"EFMA-1641100","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2921505895","display_name":null,"funder_award_id":"DMS-1908736","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3613440022","display_name":null,"funder_award_id":"DMS-1819220","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G4654238941","display_name":"From Topological Insulators to Hybrid Inverse Problems","funder_award_id":"1908736","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5008562166","display_name":null,"funder_award_id":"1641100","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6013338717","display_name":null,"funder_award_id":"DMS-1908736","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G6285244745","display_name":null,"funder_award_id":"1819220","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G964711586","display_name":null,"funder_award_id":"DMS-1819220","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4385767545.pdf","grobid_xml":"https://content.openalex.org/works/W4385767545.grobid-xml"},"referenced_works_count":38,"referenced_works":["https://openalex.org/W56293556","https://openalex.org/W326669990","https://openalex.org/W623671459","https://openalex.org/W1498458032","https://openalex.org/W1505459535","https://openalex.org/W1978067438","https://openalex.org/W1987914519","https://openalex.org/W1993896628","https://openalex.org/W2035148957","https://openalex.org/W2036840443","https://openalex.org/W2068882164","https://openalex.org/W2071340121","https://openalex.org/W2074907694","https://openalex.org/W2118368638","https://openalex.org/W2127169435","https://openalex.org/W2137549166","https://openalex.org/W2168249637","https://openalex.org/W2299847111","https://openalex.org/W2482762127","https://openalex.org/W2516802786","https://openalex.org/W2614461791","https://openalex.org/W2788850763","https://openalex.org/W2793369479","https://openalex.org/W2803667181","https://openalex.org/W2888201481","https://openalex.org/W2952176028","https://openalex.org/W2962932101","https://openalex.org/W2964267668","https://openalex.org/W3100873716","https://openalex.org/W3101118761","https://openalex.org/W3101121098","https://openalex.org/W3104493094","https://openalex.org/W3167880096","https://openalex.org/W3203652744","https://openalex.org/W4220764314","https://openalex.org/W4231706539","https://openalex.org/W4309454926","https://openalex.org/W4324055496"],"related_works":["https://openalex.org/W2035329725","https://openalex.org/W4376641153","https://openalex.org/W2050788868","https://openalex.org/W4250391473","https://openalex.org/W4302292679","https://openalex.org/W2956222435","https://openalex.org/W4241625287","https://openalex.org/W4295885776","https://openalex.org/W2031579480","https://openalex.org/W2027634686"],"abstract_inverted_index":{"Twisted":[0],"bilayer":[1],"graphene":[2],"gives":[3],"rise":[4],"to":[5,67,89,99,113,142,180],"large":[6,146],"moir\\'e":[7],"patterns":[8],"that":[9,29,152],"form":[10],"a":[11,90,96,109,127,140,145,153,160,164],"triangular":[12,22,165],"network":[13,166],"upon":[14],"mechanical":[15],"relaxation.":[16],"If":[17],"gating":[18],"is":[19,157],"included,":[20],"each":[21,48],"region":[23],"has":[24,50],"gapped":[25],"electronic":[26],"Dirac":[27],"points":[28],"behave":[30],"as":[31,163],"bulk":[32,86],"topological":[33,36],"insulators":[34],"with":[35,174],"indices":[37],"depending":[38],"on":[39],"valley":[40],"index":[41],"and":[42,76,93,130,184],"the":[43,68,85,104,121],"type":[44],"of":[45,71,78,123,148,171],"stacking.":[46],"Since":[47],"triangle":[49],"two":[51],"oppositely":[52],"charged":[53],"valleys,":[54],"they":[55],"remain":[56],"topologically":[57],"trivial.":[58],"In":[59],"this":[60,72],"work,":[61],"we":[62,83,107,138],"address":[63],"several":[64],"questions":[65],"related":[66],"edge":[69],"currents":[70,183],"system":[73],"by":[74],"analysis":[75],"computation":[77],"continuum":[79,111,149],"PDE":[80],"models.":[81],"First,":[82],"derive":[84],"invariants":[87],"corresponding":[88],"single":[91],"valley,":[92],"then":[94],"apply":[95],"bulk-interface":[97],"correspondence":[98],"quantify":[100],"asymmetric":[101,155],"transport":[102],"along":[103],"interface.":[105],"Second,":[106],"introduce":[108],"valley-coupled":[110],"model":[112],"show":[114],"how":[115,131],"valleys":[116,132],"are":[117],"approximately":[118],"decoupled":[119],"in":[120],"presence":[122],"small":[124],"perturbations":[125],"using":[126,177],"multiscale":[128],"expansion,":[129],"couple":[133],"for":[134,144],"larger":[135],"defects.":[136],"Third,":[137],"present":[139],"method":[141],"prove":[143],"class":[147],"(pseudo)differential":[150],"models":[151],"quantized":[154],"current":[156],"preserved":[158],"through":[159],"junction":[161],"such":[162],"vertex.":[167],"We":[168],"support":[169],"all":[170],"these":[172],"arguments":[173],"numerical":[175],"simulations":[176],"spectral":[178],"methods":[179],"compute":[181],"relevant":[182],"wave":[185],"packet":[186],"propagation.":[187]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
