Faithful tight-binding models and fragile topology of magic-angle bilayer graphene
Correlated insulators and superconductivity have been observed in "magic-angle" twisted bilayer graphene, when the nearly flat bands close to neutrality are partially filled. While a momentum-space continuum model accurately describes these flat bands, interaction effects are more convenie...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
American Physical Society (APS)
2021
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| Online Access: | https://hdl.handle.net/1721.1/136513 |
| _version_ | 1811076676646338560 |
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| author | Po, Hoi Chun Zou, Liujun Senthil, T Vishwanath, Ashvin |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Po, Hoi Chun Zou, Liujun Senthil, T Vishwanath, Ashvin |
| author_sort | Po, Hoi Chun |
| collection | MIT |
| description | Correlated insulators and superconductivity have been observed in "magic-angle" twisted bilayer graphene, when the nearly flat bands close to neutrality are partially filled. While a momentum-space continuum model accurately describes these flat bands, interaction effects are more conveniently incorporated in tight-binding models. We have previously shown that no fully symmetric tight-binding model can be minimal, in the sense of capturing just the flat bands, so extended models are unavoidable. Here, we introduce a family of tight-binding models that capture the flat bands while simultaneously retaining all symmetries. In particular, we construct three concrete models with five, six, or ten bands per valley and per spin. These models are also faithful, in that the additional degrees of freedom represent energy bands further away from neutrality, and they serve as optimal starting points for a controlled study of interaction effects. Furthermore, our construction demonstrates the "fragile topology" of the nearly flat bands; i.e., the obstruction to constructing exponentially localized Wannier functions can be resolved when a particular set of trivial bands is added to the model. |
| first_indexed | 2024-09-23T10:25:49Z |
| format | Article |
| id | mit-1721.1/136513 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T10:25:49Z |
| publishDate | 2021 |
| publisher | American Physical Society (APS) |
| record_format | dspace |
| spelling | mit-1721.1/1365132023-09-28T20:06:51Z Faithful tight-binding models and fragile topology of magic-angle bilayer graphene Po, Hoi Chun Zou, Liujun Senthil, T Vishwanath, Ashvin Massachusetts Institute of Technology. Department of Physics Correlated insulators and superconductivity have been observed in "magic-angle" twisted bilayer graphene, when the nearly flat bands close to neutrality are partially filled. While a momentum-space continuum model accurately describes these flat bands, interaction effects are more conveniently incorporated in tight-binding models. We have previously shown that no fully symmetric tight-binding model can be minimal, in the sense of capturing just the flat bands, so extended models are unavoidable. Here, we introduce a family of tight-binding models that capture the flat bands while simultaneously retaining all symmetries. In particular, we construct three concrete models with five, six, or ten bands per valley and per spin. These models are also faithful, in that the additional degrees of freedom represent energy bands further away from neutrality, and they serve as optimal starting points for a controlled study of interaction effects. Furthermore, our construction demonstrates the "fragile topology" of the nearly flat bands; i.e., the obstruction to constructing exponentially localized Wannier functions can be resolved when a particular set of trivial bands is added to the model. 2021-10-27T20:35:44Z 2021-10-27T20:35:44Z 2019 2021-06-24T12:20:43Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/136513 en 10.1103/PHYSREVB.99.195455 Physical Review B Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Physical Society (APS) APS |
| spellingShingle | Po, Hoi Chun Zou, Liujun Senthil, T Vishwanath, Ashvin Faithful tight-binding models and fragile topology of magic-angle bilayer graphene |
| title | Faithful tight-binding models and fragile topology of magic-angle bilayer graphene |
| title_full | Faithful tight-binding models and fragile topology of magic-angle bilayer graphene |
| title_fullStr | Faithful tight-binding models and fragile topology of magic-angle bilayer graphene |
| title_full_unstemmed | Faithful tight-binding models and fragile topology of magic-angle bilayer graphene |
| title_short | Faithful tight-binding models and fragile topology of magic-angle bilayer graphene |
| title_sort | faithful tight binding models and fragile topology of magic angle bilayer graphene |
| url | https://hdl.handle.net/1721.1/136513 |
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