{"id":"https://openalex.org/W1987705333","doi":"https://doi.org/10.1103/physrevb.76.205402","title":"Zero modes and edge states of the honeycomb lattice","display_name":"Zero modes and edge states of the honeycomb lattice","publication_year":2007,"publication_date":"2007-11-02","ids":{"openalex":"https://openalex.org/W1987705333","doi":"https://doi.org/10.1103/physrevb.76.205402","mag":"1987705333"},"language":"en","primary_location":{"id":"doi:10.1103/physrevb.76.205402","doi":"https://doi.org/10.1103/physrevb.76.205402","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physrevb.76.205402","pdf_url":null,"source":{"id":"https://openalex.org/S6791298","display_name":"Physical Review B","issn_l":"1098-0121","issn":["1098-0121","1538-4489","1550-235X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","vabb-shw"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review B","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/cond-mat/0702162","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069500436","display_name":"Mahito Kohmoto","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4405286944","display_name":"The Institute for Solid State Physics, The University of Tokyo","ror":"https://ror.org/03mpax711","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4405286944","https://openalex.org/I74801974"]},{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Mahito Kohmoto","raw_affiliation_strings":["Institute for Solid State Physics, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Solid State Physics, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581, Japan","institution_ids":["https://openalex.org/I4405286944","https://openalex.org/I74801974"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101474998","display_name":"Yasumasa Hasegawa","orcid":"https://orcid.org/0000-0003-1797-8884","observed_orcids":["https://orcid.org/0000-0003-1797-8884"]},"institutions":[{"id":"https://openalex.org/I180941496","display_name":"University of Hyogo","ror":"https://ror.org/0151bmh98","country_code":"JP","type":"education","lineage":["https://openalex.org/I180941496"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yasumasa Hasegawa","raw_affiliation_strings":["Department of Material Science, Graduate School of Material Science, University of Hyogo Ako, Hyogo 678-1297, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Material Science, Graduate School of Material Science, University of Hyogo Ako, Hyogo 678-1297, Japan","institution_ids":["https://openalex.org/I180941496"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2675,"currency":"USD","value_usd":2675},"apc_paid":null,"fwci":3.9113,"has_fulltext":true,"cited_by_count":128,"citation_normalized_percentile":{"value":0.94074757,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"76","issue":"20","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10657","display_name":"Topological Materials and Phenomena","score":0.9843999743461609,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10657","display_name":"Topological Materials and Phenomena","score":0.9843999743461609,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"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/T10382","display_name":"Quantum and electron transport phenomena","score":0.00559999980032444,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"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/T13531","display_name":"Surface and Thin Film Phenomena","score":0.0012000000569969416,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"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/honeycomb-lattice","display_name":"honeycomb lattice","score":0.9950000047683716},{"id":"https://openalex.org/keywords/edge-states","display_name":"edge states","score":0.8190000057220459},{"id":"https://openalex.org/keywords/zero-modes","display_name":"zero modes","score":0.9959999918937683},{"id":"https://openalex.org/keywords/tight-binding-model","display_name":"tight-binding model","score":0.7820000052452087},{"id":"https://openalex.org/keywords/zigzag-edge","display_name":"zigzag edge","score":0.7860000133514404},{"id":"https://openalex.org/keywords/armchair-edge","display_name":"armchair edge","score":0.9869999885559082},{"id":"https://openalex.org/keywords/cylinder-geometry","display_name":"cylinder geometry","score":0.7450000047683716},{"id":"https://openalex.org/keywords/anisotropic-systems","display_name":"anisotropic systems","score":0.6549999713897705},{"id":"https://openalex.org/keywords/localized-states","display_name":"localized states","score":0.7639999985694885},{"id":"https://openalex.org/keywords/extended-states","display_name":"extended states","score":0.8539999723434448},{"id":"https://openalex.org/keywords/graphene","display_name":"graphene","score":0.75}],"concepts":[{"id":"https://openalex.org/C192271897","wikidata":"https://www.wikidata.org/wiki/Q198438","display_name":"Zigzag","level":2,"score":0.9487712383270264},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.7201455235481262},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.645439863204956},{"id":"https://openalex.org/C85725439","wikidata":"https://www.wikidata.org/wiki/Q466686","display_name":"Anisotropy","level":2,"score":0.6370969414710999},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.5825471878051758},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5116294026374817},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.47282373905181885},{"id":"https://openalex.org/C145665481","wikidata":"https://www.wikidata.org/wiki/Q123339","display_name":"Honeycomb","level":2,"score":0.45055603981018066},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.18368414044380188},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.1710936427116394},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.05271488428115845},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1103/physrevb.76.205402","doi":"https://doi.org/10.1103/physrevb.76.205402","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physrevb.76.205402","pdf_url":null,"source":{"id":"https://openalex.org/S6791298","display_name":"Physical Review B","issn_l":"1098-0121","issn":["1098-0121","1538-4489","1550-235X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","vabb-shw"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review B","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:cond-mat/0702162","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/cond-mat/0702162","pdf_url":"https://arxiv.org/pdf/cond-mat/0702162","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.cond-mat/0702162","doi":"https://doi.org/10.48550/arxiv.cond-mat/0702162","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.cond-mat/0702162","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:cond-mat/0702162","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/cond-mat/0702162","pdf_url":"https://arxiv.org/pdf/cond-mat/0702162","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1987705333.pdf","grobid_xml":"https://content.openalex.org/works/W1987705333.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W1491016379","https://openalex.org/W1976212732","https://openalex.org/W1980235825","https://openalex.org/W1983208835","https://openalex.org/W1992266192","https://openalex.org/W1992330719","https://openalex.org/W1997401822","https://openalex.org/W2015988597","https://openalex.org/W2017988041","https://openalex.org/W2023042671","https://openalex.org/W2023319245","https://openalex.org/W2030126423","https://openalex.org/W2030628997","https://openalex.org/W2038697346","https://openalex.org/W2052976411","https://openalex.org/W2066414697","https://openalex.org/W2073047667","https://openalex.org/W2082068109","https://openalex.org/W2092831789","https://openalex.org/W2102415385","https://openalex.org/W2118492507","https://openalex.org/W2125284466"],"related_works":["https://openalex.org/W4309112554","https://openalex.org/W4221146216","https://openalex.org/W4415157778","https://openalex.org/W4405319485","https://openalex.org/W2751770864","https://openalex.org/W1999250436","https://openalex.org/W2616950942","https://openalex.org/W7163869658","https://openalex.org/W4317543167","https://openalex.org/W2963022497"],"abstract_inverted_index":{"The":[0,22],"honeycomb":[1],"lattice":[2],"in":[3],"the":[4,39,50,55],"cylinder":[5],"geometry":[6],"with":[7,25,77],"zigzag":[8,12],"edges,":[9,11],"bearded":[10,14],"and":[13,17,75],"edges":[15,19,37,52],"(zigzag-bearded),":[16],"armchair":[18,40,51],"are":[20,32],"studied.":[21],"tight-binding":[23],"model":[24],"nearest-neighbor":[26],"hoppings":[27],"is":[28,43,57],"used.":[29],"Edge":[30],"states":[31,48,60,76],"obtained":[33],"analytically":[34],"for":[35,49],"these":[36],"except":[38],"edges.":[41],"It":[42],"shown,":[44],"however,":[45],"that":[46],"edge":[47],"exist":[53],"when":[54],"system":[56],"anisotropic.":[58],"These":[59],"have":[61],"not":[62],"been":[63],"known":[64],"previously.":[65],"We":[66],"also":[67],"find":[68],"strictly":[69],"localized":[70],"states,":[71,74],"uniformly":[72],"extended":[73],"macroscopic":[78],"degeneracy.":[79]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":14},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":3}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}