Many-body ground states from decomposition of ideal higher Chern bands: Applications to chirally twisted graphene multilayers
Motivated by the higher Chern bands of twisted graphene multilayers, we consider flat bands with arbitrary Chern number C with ideal quantum geometry. While C>1 bands differ from Landau levels, we show that these bands host exact fractional Chern insulator (FCI) ground states for short-range inte...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2023-06-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.5.023166 |
| _version_ | 1797210462550491136 |
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| author | Junkai Dong Patrick J. Ledwith Eslam Khalaf Jong Yeon Lee Ashvin Vishwanath |
| author_facet | Junkai Dong Patrick J. Ledwith Eslam Khalaf Jong Yeon Lee Ashvin Vishwanath |
| author_sort | Junkai Dong |
| collection | DOAJ |
| description | Motivated by the higher Chern bands of twisted graphene multilayers, we consider flat bands with arbitrary Chern number C with ideal quantum geometry. While C>1 bands differ from Landau levels, we show that these bands host exact fractional Chern insulator (FCI) ground states for short-range interactions. We show how to decompose ideal higher Chern bands into separate ideal bands with Chern number 1 that are intertwined through translation and rotation symmetry. The decomposed bands admit an SU(C) action that combines real space and momentum space translations. Remarkably, they also allow for analytic construction of exact many-body ground states, such as generalized quantum Hall ferromagnets and FCIs, including flavor-singlet Halperin states and Laughlin ferromagnets in the limit of short-range interactions. In this limit, the SU(C) action is promoted to a symmetry on the ground-state subspace. While flavor singlet states are translation symmetric, the flavor ferromagnets correspond to translation broken states and admit charged skyrmion excitations corresponding to a spatially varying density wave pattern. We confirm our analytic predictions with numerical simulations of ideal bands of twisted chiral multilayers of graphene, and discuss consequences for experimentally accessible systems such as monolayer graphene twisted relative to a Bernal bilayer. |
| first_indexed | 2024-04-24T10:10:59Z |
| format | Article |
| id | doaj.art-b51e5efa150042c7a192158249ce8dc0 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:10:59Z |
| publishDate | 2023-06-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-b51e5efa150042c7a192158249ce8dc02024-04-12T17:31:46ZengAmerican Physical SocietyPhysical Review Research2643-15642023-06-015202316610.1103/PhysRevResearch.5.023166Many-body ground states from decomposition of ideal higher Chern bands: Applications to chirally twisted graphene multilayersJunkai DongPatrick J. LedwithEslam KhalafJong Yeon LeeAshvin VishwanathMotivated by the higher Chern bands of twisted graphene multilayers, we consider flat bands with arbitrary Chern number C with ideal quantum geometry. While C>1 bands differ from Landau levels, we show that these bands host exact fractional Chern insulator (FCI) ground states for short-range interactions. We show how to decompose ideal higher Chern bands into separate ideal bands with Chern number 1 that are intertwined through translation and rotation symmetry. The decomposed bands admit an SU(C) action that combines real space and momentum space translations. Remarkably, they also allow for analytic construction of exact many-body ground states, such as generalized quantum Hall ferromagnets and FCIs, including flavor-singlet Halperin states and Laughlin ferromagnets in the limit of short-range interactions. In this limit, the SU(C) action is promoted to a symmetry on the ground-state subspace. While flavor singlet states are translation symmetric, the flavor ferromagnets correspond to translation broken states and admit charged skyrmion excitations corresponding to a spatially varying density wave pattern. We confirm our analytic predictions with numerical simulations of ideal bands of twisted chiral multilayers of graphene, and discuss consequences for experimentally accessible systems such as monolayer graphene twisted relative to a Bernal bilayer.http://doi.org/10.1103/PhysRevResearch.5.023166 |
| spellingShingle | Junkai Dong Patrick J. Ledwith Eslam Khalaf Jong Yeon Lee Ashvin Vishwanath Many-body ground states from decomposition of ideal higher Chern bands: Applications to chirally twisted graphene multilayers Physical Review Research |
| title | Many-body ground states from decomposition of ideal higher Chern bands: Applications to chirally twisted graphene multilayers |
| title_full | Many-body ground states from decomposition of ideal higher Chern bands: Applications to chirally twisted graphene multilayers |
| title_fullStr | Many-body ground states from decomposition of ideal higher Chern bands: Applications to chirally twisted graphene multilayers |
| title_full_unstemmed | Many-body ground states from decomposition of ideal higher Chern bands: Applications to chirally twisted graphene multilayers |
| title_short | Many-body ground states from decomposition of ideal higher Chern bands: Applications to chirally twisted graphene multilayers |
| title_sort | many body ground states from decomposition of ideal higher chern bands applications to chirally twisted graphene multilayers |
| url | http://doi.org/10.1103/PhysRevResearch.5.023166 |
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