Hui Liu, Kang Yang, Ahmed Abouelkomsan, Zhao Liu, Emil J. Bergholtz
{"title":"理想陈氏带对称性的破缺","authors":"Hui Liu, Kang Yang, Ahmed Abouelkomsan, Zhao Liu, Emil J. Bergholtz","doi":"10.1103/physrevb.111.l201105","DOIUrl":null,"url":null,"abstract":"Recent observations of the fractional anomalous quantum Hall effect in moiré materials have reignited the interest in fractional Chern insulators (FCIs). The chiral limit in which analytic Landau-level-like single-particle states form an “ideal” Chern band and local interactions lead to Laughlin-like FCIs at 1</a:mn>/</a:mo>3</a:mn></a:mrow></a:math> filling has been very useful for understanding these systems by relating them to the lowest Landau level. We show, however, that, even in the idealized chiral limit, a fluctuating quantum geometry is associated with strongly broken symmetries and a phenomenology very different from that of Landau levels. In particular, particle-hole symmetry is strongly violated and, e.g., at <b:math xmlns:b=\"http://www.w3.org/1998/Math/MathML\"><b:mrow><b:mn>2</b:mn><b:mo>/</b:mo><b:mn>3</b:mn></b:mrow></b:math> filling an emergent interaction driven Fermi liquid state with no Landau level counterpart is energetically favored. In fact, even the exact Laughlin-like zero modes at <c:math xmlns:c=\"http://www.w3.org/1998/Math/MathML\"><c:mrow><c:mn>1</c:mn><c:mo>/</c:mo><c:mn>3</c:mn></c:mrow></c:math> filling have a nonuniform density tracking the underlying quantum geometry. Switching to a Coulomb interaction, the ideal Chern band with electron filling of <d:math xmlns:d=\"http://www.w3.org/1998/Math/MathML\"><d:mrow><d:mn>1</d:mn><d:mo>/</d:mo><d:mn>4</d:mn></d:mrow></d:math> features trivial charge density wave states. Moreover, applying a particle-hole transformation reveals that the ideal Chern band with hole filling of <e:math xmlns:e=\"http://www.w3.org/1998/Math/MathML\"><e:mrow><e:mn>3</e:mn><e:mo>/</e:mo><e:mn>4</e:mn></e:mrow></e:math> supports a quantum anomalous Hall crystal with quantized Hall conductance of <f:math xmlns:f=\"http://www.w3.org/1998/Math/MathML\"><f:mrow><f:msup><f:mi>e</f:mi><f:mn>2</f:mn></f:msup><f:mo>/</f:mo><f:mi>h</f:mi></f:mrow></f:math>. These phenomena have no direct lowest Landau level counterpart. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":"58 1","pages":""},"PeriodicalIF":3.7000,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Broken symmetry in ideal Chern bands\",\"authors\":\"Hui Liu, Kang Yang, Ahmed Abouelkomsan, Zhao Liu, Emil J. Bergholtz\",\"doi\":\"10.1103/physrevb.111.l201105\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Recent observations of the fractional anomalous quantum Hall effect in moiré materials have reignited the interest in fractional Chern insulators (FCIs). The chiral limit in which analytic Landau-level-like single-particle states form an “ideal” Chern band and local interactions lead to Laughlin-like FCIs at 1</a:mn>/</a:mo>3</a:mn></a:mrow></a:math> filling has been very useful for understanding these systems by relating them to the lowest Landau level. We show, however, that, even in the idealized chiral limit, a fluctuating quantum geometry is associated with strongly broken symmetries and a phenomenology very different from that of Landau levels. In particular, particle-hole symmetry is strongly violated and, e.g., at <b:math xmlns:b=\\\"http://www.w3.org/1998/Math/MathML\\\"><b:mrow><b:mn>2</b:mn><b:mo>/</b:mo><b:mn>3</b:mn></b:mrow></b:math> filling an emergent interaction driven Fermi liquid state with no Landau level counterpart is energetically favored. In fact, even the exact Laughlin-like zero modes at <c:math xmlns:c=\\\"http://www.w3.org/1998/Math/MathML\\\"><c:mrow><c:mn>1</c:mn><c:mo>/</c:mo><c:mn>3</c:mn></c:mrow></c:math> filling have a nonuniform density tracking the underlying quantum geometry. Switching to a Coulomb interaction, the ideal Chern band with electron filling of <d:math xmlns:d=\\\"http://www.w3.org/1998/Math/MathML\\\"><d:mrow><d:mn>1</d:mn><d:mo>/</d:mo><d:mn>4</d:mn></d:mrow></d:math> features trivial charge density wave states. Moreover, applying a particle-hole transformation reveals that the ideal Chern band with hole filling of <e:math xmlns:e=\\\"http://www.w3.org/1998/Math/MathML\\\"><e:mrow><e:mn>3</e:mn><e:mo>/</e:mo><e:mn>4</e:mn></e:mrow></e:math> supports a quantum anomalous Hall crystal with quantized Hall conductance of <f:math xmlns:f=\\\"http://www.w3.org/1998/Math/MathML\\\"><f:mrow><f:msup><f:mi>e</f:mi><f:mn>2</f:mn></f:msup><f:mo>/</f:mo><f:mi>h</f:mi></f:mrow></f:math>. These phenomena have no direct lowest Landau level counterpart. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>\",\"PeriodicalId\":20082,\"journal\":{\"name\":\"Physical Review B\",\"volume\":\"58 1\",\"pages\":\"\"},\"PeriodicalIF\":3.7000,\"publicationDate\":\"2025-05-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Physical Review B\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1103/physrevb.111.l201105\",\"RegionNum\":2,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Physics and Astronomy\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review B","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physrevb.111.l201105","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Physics and Astronomy","Score":null,"Total":0}
Recent observations of the fractional anomalous quantum Hall effect in moiré materials have reignited the interest in fractional Chern insulators (FCIs). The chiral limit in which analytic Landau-level-like single-particle states form an “ideal” Chern band and local interactions lead to Laughlin-like FCIs at 1/3 filling has been very useful for understanding these systems by relating them to the lowest Landau level. We show, however, that, even in the idealized chiral limit, a fluctuating quantum geometry is associated with strongly broken symmetries and a phenomenology very different from that of Landau levels. In particular, particle-hole symmetry is strongly violated and, e.g., at 2/3 filling an emergent interaction driven Fermi liquid state with no Landau level counterpart is energetically favored. In fact, even the exact Laughlin-like zero modes at 1/3 filling have a nonuniform density tracking the underlying quantum geometry. Switching to a Coulomb interaction, the ideal Chern band with electron filling of 1/4 features trivial charge density wave states. Moreover, applying a particle-hole transformation reveals that the ideal Chern band with hole filling of 3/4 supports a quantum anomalous Hall crystal with quantized Hall conductance of e2/h. These phenomena have no direct lowest Landau level counterpart. Published by the American Physical Society2025
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