Degenerate Flat Bands in Twisted Bilayer Graphene.
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| Title: | Degenerate Flat Bands in Twisted Bilayer Graphene. |
|---|---|
| Authors: | Becker, Simon1 (AUTHOR) simon.becker@math.ethz.ch, Humbert, Tristan2 (AUTHOR) tristan.humbert@ens.psl.eu, Zworski, Maciej2 (AUTHOR) zworski@math.berkeley.edu |
| Source: | Archive for Rational Mechanics & Analysis. Feb2026, Vol. 250 Issue 1, p1-45. 45p. |
| Subjects: | Graphene, Hamiltonian mechanics, Multiplicity (Mathematics), Quantum mechanics, Geometric quantum phases, Bloch's theorem |
| Abstract: | We prove that in the chiral limit of the Bistritzer–MacDonald Hamiltonian, there exist magic angles at which the Hamiltonian exhibits flat bands of multiplicity four instead of two. We analyse the structure of Bloch functions associated with the bands of arbitrary multiplicity, compute the corresponding Chern number to be - 1 , and show that there exist infinitely many degenerate magic angles for a generic choice of tunnelling potential, including the Bistritzer–MacDonald potential. Moreover, we demonstrate for generic tunnelling potentials that flat bands have only twofold or fourfold multiplicities. [ABSTRACT FROM AUTHOR] |
| Copyright of Archive for Rational Mechanics & Analysis is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 189863977 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s00205-025-02155-3 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 45 StartPage: 1 Subjects: – SubjectFull: Graphene Type: general – SubjectFull: Hamiltonian mechanics Type: general – SubjectFull: Multiplicity (Mathematics) Type: general – SubjectFull: Quantum mechanics Type: general – SubjectFull: Geometric quantum phases Type: general – SubjectFull: Bloch's theorem Type: general Titles: – TitleFull: Degenerate Flat Bands in Twisted Bilayer Graphene. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Becker, Simon – PersonEntity: Name: NameFull: Humbert, Tristan – PersonEntity: Name: NameFull: Zworski, Maciej IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 02 Text: Feb2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 00039527 Numbering: – Type: volume Value: 250 – Type: issue Value: 1 Titles: – TitleFull: Archive for Rational Mechanics & Analysis Type: main |
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