{"id":"https://openalex.org/W2036051189","doi":"https://doi.org/10.1088/0957-4484/19/43/435401","title":"Dirac equation description of the electronic states and magnetic properties of a square graphene quantum dot","display_name":"Dirac equation description of the electronic states and magnetic properties of a square graphene quantum dot","publication_year":2008,"publication_date":"2008-09-22","ids":{"openalex":"https://openalex.org/W2036051189","doi":"https://doi.org/10.1088/0957-4484/19/43/435401","mag":"2036051189","pmid":"https://pubmed.ncbi.nlm.nih.gov/21832693"},"language":"en","primary_location":{"id":"doi:10.1088/0957-4484/19/43/435401","doi":"https://doi.org/10.1088/0957-4484/19/43/435401","is_oa":false,"landing_page_url":"https://doi.org/10.1088/0957-4484/19/43/435401","pdf_url":null,"source":{"id":"https://openalex.org/S206811868","display_name":"Nanotechnology","issn_l":"0957-4484","issn":["0957-4484","1361-6528"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-2","ki-jl-1","medline","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Nanotechnology","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0811.4312","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102102253","display_name":"Changlin Tang","orcid":"https://orcid.org/0009-0001-2934-4814","observed_orcids":["https://orcid.org/0009-0001-2934-4814","https://orcid.org/0009-0007-7532-341X"]},"institutions":[{"id":"https://openalex.org/I194450716","display_name":"Jilin University","ror":"https://ror.org/00js3aw79","country_code":"CN","type":"education","lineage":["https://openalex.org/I194450716"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210119098","display_name":"Fujian Institute of Research on the Structure of Matter","ror":"https://ror.org/02j89k719","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210119098"]},{"id":"https://openalex.org/I4391767757","display_name":"State Key Laboratory of Structural Chemistry","ror":"https://ror.org/023fpv336","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210119098","https://openalex.org/I4391767757"]},{"id":"https://openalex.org/I4391768279","display_name":"State Key Laboratory of High Pressure and Superhard Materials","ror":"https://ror.org/03sjvjt84","country_code":"CN","type":"facility","lineage":["https://openalex.org/I194450716","https://openalex.org/I4391768279"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Changlin Tang","raw_affiliation_strings":["National Laboratory of Superhard Materials, Department of Physics, Jilin University, Changchun 130023, People's Republic of China. State Key Lab of Structural Chemistry, Fujian Institute of Research on the Structure of Matter and Graduate School of Chinese Academy of Sciences, Fuzhou 350002, People's Republic of China","National Laboratory of Superhard Materials, Department of Physics, Jilin University, Changchun 130023, People\u2019s Republic of China","State Key Lab of Structural Chemistry, Fujian Institute of Research on the Structure of Matter and Graduate School of Chinese Academy of Sciences, Fuzhou 350002, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Laboratory of Superhard Materials, Department of Physics, Jilin University, Changchun 130023, People's Republic of China. State Key Lab of Structural Chemistry, Fujian Institute of Research on the Structure of Matter and Graduate School of Chinese Academy of Sciences, Fuzhou 350002, People's Republic of China","institution_ids":["https://openalex.org/I194450716","https://openalex.org/I19820366","https://openalex.org/I4210119098","https://openalex.org/I4391767757","https://openalex.org/I4391768279"]},{"raw_affiliation_string":"National Laboratory of Superhard Materials, Department of Physics, Jilin University, Changchun 130023, People\u2019s Republic of China","institution_ids":["https://openalex.org/I194450716"]},{"raw_affiliation_string":"State Key Lab of Structural Chemistry, Fujian Institute of Research on the Structure of Matter and Graduate School of Chinese Academy of Sciences, Fuzhou 350002, People\u2019s Republic of China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210119098","https://openalex.org/I4391767757"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Weihua Yan","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I194450716","display_name":"Jilin University","ror":"https://ror.org/00js3aw79","country_code":"CN","type":"education","lineage":["https://openalex.org/I194450716"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Weihua Yan","raw_affiliation_strings":["National Laboratory of Superhard Materials, Department of Physics, Jilin University,#N#Changchun 130023,#N#People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Laboratory of Superhard Materials, Department of Physics, Jilin University,#N#Changchun 130023,#N#People\u2019s Republic of China","institution_ids":["https://openalex.org/I194450716"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043525582","display_name":"Yisong Zheng","orcid":"https://orcid.org/0000-0003-2532-9171","observed_orcids":["https://orcid.org/0000-0003-2532-9171"]},"institutions":[{"id":"https://openalex.org/I194450716","display_name":"Jilin University","ror":"https://ror.org/00js3aw79","country_code":"CN","type":"education","lineage":["https://openalex.org/I194450716"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yisong Zheng","raw_affiliation_strings":["National Laboratory of Superhard Materials, Department of Physics, Jilin University,#N#Changchun 130023,#N#People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Laboratory of Superhard Materials, Department of Physics, Jilin University,#N#Changchun 130023,#N#People\u2019s Republic of China","institution_ids":["https://openalex.org/I194450716"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111846994","display_name":"Guangshe Li","orcid":"https://orcid.org/0000-0001-8592-8729","observed_orcids":["https://orcid.org/0000-0001-8592-8729","https://orcid.org/0000-0002-3278-1804","https://orcid.org/0000-0001-5720-2031"]},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210119098","display_name":"Fujian Institute of Research on the Structure of Matter","ror":"https://ror.org/02j89k719","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210119098"]},{"id":"https://openalex.org/I4391767757","display_name":"State Key Laboratory of Structural Chemistry","ror":"https://ror.org/023fpv336","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210119098","https://openalex.org/I4391767757"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guangshe Li","raw_affiliation_strings":["State Key Lab of Structural Chemistry, Fujian Institute of Research on the Structure of Matter, and Graduate School of Chinese Academy of Sciences, Fuzhou 350002, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Lab of Structural Chemistry, Fujian Institute of Research on the Structure of Matter, and Graduate School of Chinese Academy of Sciences, Fuzhou 350002, People\u2019s Republic of China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210119098","https://openalex.org/I4391767757"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068260708","display_name":"Liping Li","orcid":"https://orcid.org/0000-0002-6732-4902","observed_orcids":["https://orcid.org/0000-0002-6732-4902"]},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210119098","display_name":"Fujian Institute of Research on the Structure of Matter","ror":"https://ror.org/02j89k719","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210119098"]},{"id":"https://openalex.org/I4391767757","display_name":"State Key Laboratory of Structural Chemistry","ror":"https://ror.org/023fpv336","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210119098","https://openalex.org/I4391767757"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liping Li","raw_affiliation_strings":["State Key Lab of Structural Chemistry, Fujian Institute of Research on the Structure of Matter, and Graduate School of Chinese Academy of Sciences, Fuzhou 350002, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Lab of Structural Chemistry, Fujian Institute of Research on the Structure of Matter, and Graduate School of Chinese Academy of Sciences, Fuzhou 350002, People\u2019s Republic of China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210119098","https://openalex.org/I4391767757"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3325,"currency":"USD","value_usd":3325},"apc_paid":null,"fwci":1.5907,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.82206714,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":99},"biblio":{"volume":"19","issue":"43","first_page":"435401","last_page":"435401"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10083","display_name":"Graphene research and applications","score":0.9789999723434448,"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":0.9789999723434448,"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/T10382","display_name":"Quantum and electron transport phenomena","score":0.005100000184029341,"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/T10275","display_name":"2D Materials and Applications","score":0.0027000000700354576,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/graphene-quantum-dots","display_name":"graphene quantum dots","score":0.9409999847412109},{"id":"https://openalex.org/keywords/dirac-equation","display_name":"Dirac equation","score":0.9670000076293945},{"id":"https://openalex.org/keywords/zigzag-edge","display_name":"zigzag edge","score":0.621999979019165},{"id":"https://openalex.org/keywords/armchair-edge","display_name":"armchair edge","score":1.0},{"id":"https://openalex.org/keywords/surface-states","display_name":"surface states","score":0.7639999985694885},{"id":"https://openalex.org/keywords/magnetic-properties","display_name":"magnetic properties","score":0.7289999723434448},{"id":"https://openalex.org/keywords/magnetic-order","display_name":"magnetic ordering","score":0.9509999752044678},{"id":"https://openalex.org/keywords/critical-size","display_name":"critical size","score":0.7889999747276306},{"id":"https://openalex.org/keywords/two-state-model","display_name":"two-state model","score":0.753000020980835},{"id":"https://openalex.org/keywords/size-effect","display_name":"size effect","score":0.5630000233650208},{"id":"https://openalex.org/keywords/hartree-fock-mean-field","display_name":"Hartree-Fock mean field","score":0.8080000281333923}],"concepts":[{"id":"https://openalex.org/C2778323463","wikidata":"https://www.wikidata.org/wiki/Q19597372","display_name":"Graphene quantum dot","level":3,"score":0.7180913686752319},{"id":"https://openalex.org/C30080830","wikidata":"https://www.wikidata.org/wiki/Q169917","display_name":"Graphene","level":2,"score":0.6912730932235718},{"id":"https://openalex.org/C192271897","wikidata":"https://www.wikidata.org/wiki/Q198438","display_name":"Zigzag","level":2,"score":0.6769895553588867},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.6478134393692017},{"id":"https://openalex.org/C82601208","wikidata":"https://www.wikidata.org/wiki/Q272621","display_name":"Dirac equation","level":2,"score":0.6367416381835938},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.5588191747665405},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5280968546867371},{"id":"https://openalex.org/C124657808","wikidata":"https://www.wikidata.org/wiki/Q1133068","display_name":"Quantum dot","level":2,"score":0.5077982544898987},{"id":"https://openalex.org/C69523127","wikidata":"https://www.wikidata.org/wiki/Q4480008","display_name":"Ground state","level":2,"score":0.4893190562725067},{"id":"https://openalex.org/C115260700","wikidata":"https://www.wikidata.org/wiki/Q11408","display_name":"Magnetic field","level":2,"score":0.4598698318004608},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.43896016478538513},{"id":"https://openalex.org/C61039578","wikidata":"https://www.wikidata.org/wiki/Q604279","display_name":"Dirac (video compression format)","level":3,"score":0.42715543508529663},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.4047333002090454},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07444959878921509},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.0},{"id":"https://openalex.org/C186453547","wikidata":"https://www.wikidata.org/wiki/Q2126","display_name":"Neutrino","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1088/0957-4484/19/43/435401","doi":"https://doi.org/10.1088/0957-4484/19/43/435401","is_oa":false,"landing_page_url":"https://doi.org/10.1088/0957-4484/19/43/435401","pdf_url":null,"source":{"id":"https://openalex.org/S206811868","display_name":"Nanotechnology","issn_l":"0957-4484","issn":["0957-4484","1361-6528"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-2","ki-jl-1","medline","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Nanotechnology","raw_type":"journal-article"},{"id":"pmid:21832693","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/21832693","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Nanotechnology","raw_type":"Journal Article"},{"id":"pmh:oai:arXiv.org:0811.4312","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/0811.4312","pdf_url":"https://arxiv.org/pdf/0811.4312","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.0811.4312","doi":"https://doi.org/10.48550/arxiv.0811.4312","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.0811.4312","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:0811.4312","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/0811.4312","pdf_url":"https://arxiv.org/pdf/0811.4312","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1491016379","https://openalex.org/W1505656046","https://openalex.org/W1535106284","https://openalex.org/W1967202721","https://openalex.org/W1973840913","https://openalex.org/W1974756907","https://openalex.org/W1994255514","https://openalex.org/W1998323434","https://openalex.org/W2014935324","https://openalex.org/W2025170659","https://openalex.org/W2030628997","https://openalex.org/W2038697346","https://openalex.org/W2058122340","https://openalex.org/W2066009637","https://openalex.org/W2068824512","https://openalex.org/W2072923279","https://openalex.org/W2079468187","https://openalex.org/W2084025640","https://openalex.org/W2086349876","https://openalex.org/W2090145840","https://openalex.org/W2113841783","https://openalex.org/W2118492507","https://openalex.org/W2119882629","https://openalex.org/W2122704104","https://openalex.org/W2125284466","https://openalex.org/W2139754676","https://openalex.org/W2141260394"],"related_works":["https://openalex.org/W2766358559","https://openalex.org/W2144092302","https://openalex.org/W2070675983","https://openalex.org/W3113682047","https://openalex.org/W2082672516","https://openalex.org/W2384158235","https://openalex.org/W1970697821","https://openalex.org/W2047162745","https://openalex.org/W2008669545","https://openalex.org/W2027352491"],"abstract_inverted_index":{"Electronic":[0],"eigenstates":[1],"of":[2,22,37,70,83,98,115,127,147,193],"a":[3,38,50,112,138,148,154,182],"square":[4,105,199],"graphene":[5],"quantum":[6],"dot":[7],"(GQD)":[8],"terminated":[9],"by":[10],"both":[11],"zigzag":[12,121],"and":[13,67],"armchair":[14],"edges":[15,122],"are":[16,76],"derived":[17],"in":[18,103,197],"the":[19,23,29,34,56,65,71,80,84,88,95,99,116,119,125,128,133,142,161,166,172,177,190,194,198],"theoretical":[20],"framework":[21],"Dirac":[24,30,57,173],"equation.":[25],"We":[26,107],"find":[27,108],"that":[28,109],"equation":[31,58,174],"can":[32,61,187],"determine":[33],"eigenenergy":[35],"spectrum":[36],"GQD":[39,151],"with":[40,79,160],"high":[41],"accuracy":[42],"even":[43],"if":[44],"its":[45],"size":[46,96,114,191],"is":[47],"reduced":[48],"to":[49,123,153],"few":[51],"nanometers.":[52],"More":[53],"importantly,":[54],"from":[55,165],"description":[59],"we":[60,93,180],"readily":[62],"work":[63],"out":[64],"number":[66],"energy":[68,146],"gap":[69],"conjugate":[72],"surface":[73,178],"states,":[74],"which":[75,186],"intimately":[77],"associated":[78],"magnetic":[81,100,130,143,195],"properties":[82],"GQD.":[85,106,200],"By":[86],"using":[87],"Hartree-Fock":[89],"mean":[90],"field":[91],"approach,":[92],"study":[94],"dependence":[97,192],"ordering":[101,196],"formation":[102],"this":[104],"there":[110],"exists":[111],"critical":[113],"width":[117,139],"between":[118],"two":[120],"indicate":[124],"onset":[126],"stable":[129],"ordering.":[131],"On":[132],"other":[134],"hand,":[135],"when":[136],"such":[137],"increases":[140],"further,":[141],"ground":[144],"state":[145],"charge":[149],"neutral":[150],"tends":[152],"saturated":[155],"value.":[156],"These":[157],"results":[158,163],"coincide":[159],"previous":[162],"obtained":[164],"first-principles":[167],"calculation.":[168],"Then,":[169],"based":[170],"on":[171],"solution":[175],"about":[176],"state,":[179],"establish":[181],"simple":[183],"two-state":[184],"model":[185],"quantitatively":[188],"explain":[189]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":6},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}