{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,23]],"date-time":"2026-10-23T19:53:55Z","timestamp":1792785235568,"version":"4.5.0"},"reference-count":59,"publisher":"National Academy of Sciences","issue":"41","license":[{"start":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T00:00:00Z","timestamp":1791158400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100006151","name":"DOE | SC | Basic Energy Sciences","doi-asserted-by":"publisher","award":["DE-AC02-76SF00515"],"award-info":[{"award-number":["DE-AC02-76SF00515"]}],"id":[{"id":"10.13039\/100006151","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Natural Science Foundation of China","award":["12074276"],"award-info":[{"award-number":["12074276"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"crossref"}]},{"DOI":"10.13039\/100000086","name":"NSF | Directorate for Mathematical and Physical Sciences","doi-asserted-by":"publisher","award":["DMR-2128556"],"award-info":[{"award-number":["DMR-2128556"]}],"id":[{"id":"10.13039\/100000086","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.pnas.org"],"crossmark-restriction":true},"short-container-title":["Proc. Natl. Acad. Sci. U.S.A."],"published-print":{"date-parts":[[2026,10,13]]},"abstract":"<jats:p>\n                    When a Chern band is partially filled, a fractional Chern insulator (FCI)\u2014the lattice analog of a fractional quantum Hall state\u2014can arise. Though the full range of possible scenarios for producing such a state is not established, the most tractable models combine strong electronic interactions with the quantum geometry of the parent Chern band meeting specific criteria. In twisted bilayer graphene, the importance of interactions can be tuned by varying the interlayer twist. Here, we study a sample with twist near 1.4\n                    <jats:sup>\u00b0<\/jats:sup>\n                    , large enough to suppress the zero-field correlated states. We find that applying a strong magnetic field restores the importance of electron\u2013electron interactions: at nearly half a magnetic flux quantum per moir\u00e9 unit cell, deep in the Hofstadter regime, odd-denominator fractional states appear in multiple Hofstadter subbands. These fractional states persist over larger ranges of density, and are more robustly quantized, than nearby integer states, opposite to what is seen in other fractional quantum Hall and FCI systems.\n                  <\/jats:p>","DOI":"10.1073\/pnas.2602080123","type":"journal-article","created":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T19:03:46Z","timestamp":1791227026000},"update-policy":"https:\/\/doi.org\/10.1073\/pnas.cm10313","source":"Crossref","is-referenced-by-count":0,"title":["Extended fractional Hofstadter states at high field in twisted bilayer graphene above the magic angle"],"prefix":"10.1073","volume":"123","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7166-9754","authenticated-orcid":false,"given":"Joe","family":"Finney","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00f54p054","id-type":"ROR","asserted-by":"publisher"}],"name":"Department of Physics, Stanford 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A.","family":"Kastner","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00f54p054","id-type":"ROR","asserted-by":"publisher"}],"name":"Department of Physics, Stanford University","place":["Stanford"]},{"id":[{"id":"https:\/\/ror.org\/05gzmn429","id-type":"ROR","asserted-by":"publisher"}],"name":"Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory","place":["Menlo Park"]},{"id":[{"id":"https:\/\/ror.org\/042nb2s44","id-type":"ROR","asserted-by":"publisher"}],"name":"Department of Physics, Massachusetts Institute of Technology","place":["Cambridge"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Oskar","family":"Vafek","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03s53g630","id-type":"ROR","asserted-by":"publisher"}],"name":"National High Magnetic Field 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Waters Interplay of electronic crystals with integer and fractional Chern insulators in moir\u00e9 pentalayer graphene arXiv [Preprint] (2024). https:\/\/arxiv.org\/abs\/2408.10133."},{"key":"e_1_3_4_18_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41586-025-08621-y"},{"key":"e_1_3_4_19_2","doi-asserted-by":"publisher","DOI":"10.1038\/nature26154"},{"key":"e_1_3_4_20_2","doi-asserted-by":"publisher","DOI":"10.1038\/nature26160"},{"key":"e_1_3_4_21_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.aav1910"},{"key":"e_1_3_4_22_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.aaw3780"},{"key":"e_1_3_4_23_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41563-020-00840-0"},{"key":"e_1_3_4_24_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41567-020-0906-9"},{"key":"e_1_3_4_25_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41567-021-01347-4"},{"key":"e_1_3_4_26_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41567-020-01129-4"},{"key":"e_1_3_4_27_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.abb8754"},{"key":"e_1_3_4_28_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2100006118"},{"key":"e_1_3_4_29_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.127.197701"},{"key":"e_1_3_4_30_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.127.027601"},{"key":"e_1_3_4_31_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.84.035440"},{"key":"e_1_3_4_32_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.14.2239"},{"key":"e_1_3_4_33_2","doi-asserted-by":"publisher","DOI":"10.1038\/nature12186"},{"key":"e_1_3_4_34_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.1237240"},{"key":"e_1_3_4_35_2","doi-asserted-by":"publisher","DOI":"10.1038\/nature12187"},{"key":"e_1_3_4_36_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.aad2102"},{"key":"e_1_3_4_37_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.128.217701"},{"key":"e_1_3_4_38_2","article-title":"Narrow bands in magnetic field and strong-coupling hofstadter spectra","volume":"106","author":"Wang X.","year":"2022","unstructured":"X. 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Pinczuk Perspectives in Quantum Hall Effects. (John Wiley & Sons Ltd ed. 1 1996). https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/9783527617258.","DOI":"10.1002\/9783527617258"},{"key":"e_1_3_4_51_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.39.8525"},{"key":"e_1_3_4_52_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.107.075123"},{"key":"e_1_3_4_53_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.107.075408"},{"key":"e_1_3_4_54_2","doi-asserted-by":"publisher","DOI":"10.1103\/s3s7-513d"},{"key":"e_1_3_4_55_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.104.075401"},{"key":"e_1_3_4_56_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.124.097601"},{"key":"e_1_3_4_57_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41567-023-01939-2"},{"key":"e_1_3_4_58_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.53.15845"},{"key":"e_1_3_4_59_2","unstructured":"J. Finney Data for: Extended fractional Hofstadter states at high field in twisted bilayer graphene above the magic angle Version 1.0 Stanford Digital Repository (2026). https:\/\/doi.org\/10.25740\/rs629jy3007."}],"container-title":["Proceedings of the National Academy of Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pnas.org\/doi\/pdf\/10.1073\/pnas.2602080123","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T19:04:34Z","timestamp":1791227074000},"score":1,"resource":{"primary":{"URL":"https:\/\/pnas.org\/doi\/10.1073\/pnas.2602080123"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10,5]]},"references-count":59,"journal-issue":{"issue":"41","published-print":{"date-parts":[[2026,10,13]]}},"alternative-id":["10.1073\/pnas.2602080123"],"URL":"https:\/\/doi.org\/10.1073\/pnas.2602080123","relation":{},"ISSN":["0027-8424","1091-6490"],"issn-type":[{"value":"0027-8424","type":"print"},{"value":"1091-6490","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,10,5]]},"assertion":[{"value":"2026-01-26","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-09-10","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-10-05","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e2602080123"}}