Band structure of twisted bilayer graphene: Emergent symmetries, commensurate approximants, and Wannier obstructions
A remarkable feature of the band structure of bilayer graphene at small twist angle is the appearance of isolated bands near neutrality, whose bandwidth can be reduced at certain magic angles (e.g. θ∼1.05[superscript ∘]). In this regime, correlated insulating states and superconductivity have been e...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2018
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| Online Access: | http://hdl.handle.net/1721.1/117660 |
| _version_ | 1811091979269832704 |
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| author | Zou, Liujun Po, Hoi Chun Vishwanath, Ashvin Senthil, T. |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Zou, Liujun Po, Hoi Chun Vishwanath, Ashvin Senthil, T. |
| author_sort | Zou, Liujun |
| collection | MIT |
| description | A remarkable feature of the band structure of bilayer graphene at small twist angle is the appearance of isolated bands near neutrality, whose bandwidth can be reduced at certain magic angles (e.g. θ∼1.05[superscript ∘]). In this regime, correlated insulating states and superconductivity have been experimentally observed. A microscopic description of these phenomena requires an understanding of universal aspects of the band structure, which we discuss here. First, we point out the importance of emergent symmetries, such as valley conservation, which are excellent symmetries in the limit of small twist angles and dictate qualitative features of the band structure. These have sometimes been overlooked when discussing commensurate approximants to the band structure, which we also review here, and solidify their connection with the continuum theory which incorporates all emergent symmetries. Finally, we discuss obstructions to writing tight-binding models of just the isolated bands, and in particular a symmetry-based diagnostic of these obstructions, as well as relations to band topology and strategies for resolving the obstruction. Especially, we construct a four-band model where the two lower isolated bands realize all identified Wannier obstructions of the single-valley nearly flat bands of twisted bilayer graphene. |
| first_indexed | 2024-09-23T15:10:59Z |
| format | Article |
| id | mit-1721.1/117660 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T15:10:59Z |
| publishDate | 2018 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1176602022-09-29T13:14:00Z Band structure of twisted bilayer graphene: Emergent symmetries, commensurate approximants, and Wannier obstructions Zou, Liujun Po, Hoi Chun Vishwanath, Ashvin Senthil, T. Massachusetts Institute of Technology. Department of Physics Zou, Liujun Senthil, T. A remarkable feature of the band structure of bilayer graphene at small twist angle is the appearance of isolated bands near neutrality, whose bandwidth can be reduced at certain magic angles (e.g. θ∼1.05[superscript ∘]). In this regime, correlated insulating states and superconductivity have been experimentally observed. A microscopic description of these phenomena requires an understanding of universal aspects of the band structure, which we discuss here. First, we point out the importance of emergent symmetries, such as valley conservation, which are excellent symmetries in the limit of small twist angles and dictate qualitative features of the band structure. These have sometimes been overlooked when discussing commensurate approximants to the band structure, which we also review here, and solidify their connection with the continuum theory which incorporates all emergent symmetries. Finally, we discuss obstructions to writing tight-binding models of just the isolated bands, and in particular a symmetry-based diagnostic of these obstructions, as well as relations to band topology and strategies for resolving the obstruction. Especially, we construct a four-band model where the two lower isolated bands realize all identified Wannier obstructions of the single-valley nearly flat bands of twisted bilayer graphene. United States. Department of Energy (Grant DESC0008739) National Science Foundation (U.S.) (Grant 1411343) 2018-09-06T19:53:33Z 2018-09-06T19:53:33Z 2018-08 2018-06 2018-08-28T18:00:28Z Article http://purl.org/eprint/type/JournalArticle 2469-9950 2469-9969 http://hdl.handle.net/1721.1/117660 Zou, Liujun et al. "Band structure of twisted bilayer graphene: Emergent symmetries, commensurate approximants, and Wannier obstructions." Physical Review B 98, 8 (August 2018): 085435 © 2018 American Physical Society en http://dx.doi.org/10.1103/PhysRevB.98.085435 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. American Physical Society application/pdf American Physical Society American Physical Society |
| spellingShingle | Zou, Liujun Po, Hoi Chun Vishwanath, Ashvin Senthil, T. Band structure of twisted bilayer graphene: Emergent symmetries, commensurate approximants, and Wannier obstructions |
| title | Band structure of twisted bilayer graphene: Emergent symmetries, commensurate approximants, and Wannier obstructions |
| title_full | Band structure of twisted bilayer graphene: Emergent symmetries, commensurate approximants, and Wannier obstructions |
| title_fullStr | Band structure of twisted bilayer graphene: Emergent symmetries, commensurate approximants, and Wannier obstructions |
| title_full_unstemmed | Band structure of twisted bilayer graphene: Emergent symmetries, commensurate approximants, and Wannier obstructions |
| title_short | Band structure of twisted bilayer graphene: Emergent symmetries, commensurate approximants, and Wannier obstructions |
| title_sort | band structure of twisted bilayer graphene emergent symmetries commensurate approximants and wannier obstructions |
| url | http://hdl.handle.net/1721.1/117660 |
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