{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,28]],"date-time":"2026-09-28T03:35:50Z","timestamp":1790566550833,"version":"4.1.0"},"reference-count":63,"publisher":"American Physical Society (APS)","issue":"4","license":[{"start":{"date-parts":[[2020,1,30]],"date-time":"2020-01-30T00:00:00Z","timestamp":1580342400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/link.aps.org\/licenses\/aps-default-license"},{"start":{"date-parts":[[2021,1,29]],"date-time":"2021-01-29T00:00:00Z","timestamp":1611878400000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/link.aps.org\/licenses\/aps-default-accepted-manuscript-license"}],"funder":[{"DOI":"10.13039\/100007739","name":"Aspen Center for Physics","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100007739","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["PHY-1607611"],"award-info":[{"award-number":["PHY-1607611"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Laboratory for Physical Sciences"}],"content-domain":{"domain":["journals.aps.org"],"crossmark-restriction":true},"short-container-title":["Phys. Rev. Lett."],"DOI":"10.1103\/physrevlett.124.046403","type":"journal-article","created":{"date-parts":[[2020,1,30]],"date-time":"2020-01-30T10:09:46Z","timestamp":1580378986000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":137,"title":["Collective Excitations of Quantum Anomalous Hall Ferromagnets in Twisted Bilayer Graphene"],"prefix":"10.1103","volume":"124","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1185-0073","authenticated-orcid":true,"given":"Fengcheng","family":"Wu","sequence":"first","affiliation":[{"name":"Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20742, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0439-986X","authenticated-orcid":true,"given":"Sankar","family":"Das Sarma","sequence":"additional","affiliation":[{"name":"Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20742, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"16","published-online":{"date-parts":[[2020,1,30]]},"reference":[{"key":"PhysRevLett.124.046403Cc1R1","doi-asserted-by":"publisher","DOI":"10.1038\/nature26160","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc2R1","doi-asserted-by":"publisher","DOI":"10.1038\/nature26154","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc3R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41586-019-1431-9","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc4R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41567-019-0606-5","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc5R1","unstructured":"Y. Cao, D. Chowdhury, D. Rodan-Legrain, O. Rubies-Bigord\u00e0, K. Watanabe, T. Taniguchi, T. Senthil, and P. Jarillo-Herrero, arXiv:1901.03710 [Phys. Rev. Lett. (to be published)].","type":"other"},{"key":"PhysRevLett.124.046403Cc6R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41567-019-0596-3","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc7R1","doi-asserted-by":"publisher","DOI":"10.1126\/science.aaw3780","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc8R1","doi-asserted-by":"publisher","DOI":"10.1126\/science.aay5533","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc10R1","doi-asserted-by":"publisher","DOI":"10.1126\/science.aav1910","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc12R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41586-019-1695-0","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc13R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.123.046601","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc14R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41586-019-1422-x","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc15R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41586-019-1460-4","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc19R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.121.087001","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc20R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.8.031089","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc21R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.8.031087","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc22R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.8.031088","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc23R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.121.217001","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc24R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.98.075154","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc25R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.8.041041","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc26R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41535-019-0153-4","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc27R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.99.094521","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc28R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.98.235158","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc29R1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1810947115","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc30R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.122.026801","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc31R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.98.195101","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc32R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.121.146801","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc33R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.122.106405","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc34R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.9.021013","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc35R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.123.036401","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc36R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.99.035111","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc37R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.98.205151","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc38R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.122.246401","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc39R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.122.246402","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc40R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.100.085136","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc41R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.98.220504","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc42R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.122.257002","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc43R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.98.241412","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc44R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.121.257001","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc45R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.99.165112","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc46R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.99.195114","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc47R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.99.220507","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc49R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.99.075127","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc50R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.122.016401","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc51R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.122.086402","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc54R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.1.033126","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc55R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.9.031021","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc56R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-019-12981-1","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc57R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.100.024421","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc58R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.9.031049","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc60R1","unstructured":"A. Julku, T.\u2009J. Peltonen, L. Liang, T.\u2009T. Heikkil\u00e4, and P. T\u00f6rm\u00e4, arXiv:1906.06313 [Phys. Rev. B (to be published)].","type":"other"},{"key":"PhysRevLett.124.046403Cc61R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.123.237002","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc63R1","doi-asserted-by":"publisher","DOI":"10.1126\/science.1234414","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc64R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.51.5138","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc65R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.74.075423","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc66R1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1108174108","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc67R1","unstructured":"See Supplemental Material at http:\/\/link.aps.org\/supplemental\/10.1103\/PhysRevLett.124.046403 for details of the TBG moir\u00e9 Hamiltonian and an analysis of QAHF in TBG that is closely aligned to both the top and bottom encapsulating hBN layers.","type":"other"},{"key":"PhysRevLett.124.046403Cc68R1","doi-asserted-by":"publisher","DOI":"10.1126\/science.1237240","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc69R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.115.166802","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc70R1","volume-title":"Topological Aspects of Low Dimensional Systems","author":"S.\u2009M. Girvin","year":"1999","type":"book"},{"key":"PhysRevLett.124.046403Cc71R1","volume-title":"Principles of Condensed Matter Physics","author":"P. Chaikin","year":"2000","type":"book"},{"key":"PhysRevLett.124.046403Cc72R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.113.116803","type":"journal-article"},{"key":"PhysRevLett.124.046403Cc73R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.105.266405","type":"journal-article"}],"container-title":["Physical Review Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.aps.org\/accepted\/10.1103\/PhysRevLett.124.046403","content-type":"application\/pdf","content-version":"am","intended-application":"unspecified"},{"URL":"https:\/\/link.aps.org\/article\/10.1103\/PhysRevLett.124.046403","content-type":"unspecified","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/harvest.aps.org\/v2\/journals\/articles\/10.1103\/PhysRevLett.124.046403\/fulltext","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,8,18]],"date-time":"2025-08-18T17:29:27Z","timestamp":1755538167000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.aps.org\/doi\/10.1103\/PhysRevLett.124.046403"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,30]]},"references-count":63,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2020,1]]}},"URL":"https:\/\/doi.org\/10.1103\/physrevlett.124.046403","relation":{},"ISSN":["0031-9007","1079-7114"],"issn-type":[{"value":"0031-9007","type":"print"},{"value":"1079-7114","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,1,30]]},"assertion":[{"value":"2019-08-20","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"\u00a9 2020 American Physical Society. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright_statement","label":"Copyright statement","group":{"name":"copyright","label":"copyright"}},{"value":"2020","name":"copyright_year","label":"Copyright year","group":{"name":"copyright","label":"copyright"}},{"value":"American Physical Society","name":"copyright_holder","label":"Copyright holder","group":{"name":"copyright","label":"copyright"}}],"article-number":"046403"}}