Journal article : Review
Mean-field modeling of moiré materials: a user's guide with selected applications to twisted bilayer graphene
- Abstract:
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We review the theoretical modeling of moiré materials, focusing on various aspects of magic-angle twisted bilayer graphene (MA-TBG) viewed through the lens of Hartree–Fock mean-field theory. We first provide an elementary introduction to the continuum modeling of moiré bandstructures, and explain how interactions are incorporated to study correlated states. We then discuss how to implement mean-field simulations of ground state structure and collective excitations in this setting. With this background established, we rationalize the power of mean-field approximations in MA-TBG, by discussing the idealized ‘chiral-flat’ strong-coupling limit, in which ground states at electron densities commensurate with the moiré superlattice are exactly captured by mean-field ansätze. We then illustrate the phenomenological shortcomings of this limit, leading us naturally into a discussion of the intermediate-coupling incommensurate Kekulé spiral (IKS) order and its origins in ever-present heterostrain. IKS and its placement within an expanded Hartree–Fock manifold form our first ‘case study’. Our second case study involves time-dependence, and focuses on the collective modes of various broken-symmetry insulators in MA-TBG. As a third and final case study, we return to the strong-coupling picture, which can be stabilized by aligning MA-TBG to an hBN substrate. In this limit, we show how mean field theory can be adapted to the translationally non-invariant setting in order to quantitatively study the energetics of domain walls in orbital Chern insulating states. We close with a discussion of extensions and further applications. Used either as a standalone reference or alongside the accompanying open-source code, this review should enable readers with a basic knowledge of band theory and many-body physics to systematically build and analyze detailed models of generic moiré systems.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
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(Preview, Accepted manuscript, pdf, 4.5MB, Terms of use)
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- Publisher copy:
- 10.1080/00018732.2025.2600658
Authors
- Funder identifier:
- https://ror.org/0472cxd90
- Grant:
- 804213
- Funder identifier:
- https://ror.org/001aqnf71
- Grant:
- EP/Z002419/1
- Funder identifier:
- https://ror.org/0439y7842
- Grant:
- EP/S020527/1
- EP/X030881/1
- Publisher:
- Taylor and Francis
- Journal:
- Advances in Physics More from this journal
- Volume:
- 74
- Issue:
- 1-4
- Pages:
- 11-96
- Publication date:
- 2025-12-22
- Acceptance date:
- 2025-12-01
- DOI:
- EISSN:
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1460-6976
- ISSN:
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0001-8732
- Language:
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English
- Keywords:
- Subtype:
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Review
- Pubs id:
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2355606
- Local pid:
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pubs:2355606
- Deposit date:
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2026-01-07
- ARK identifier:
Terms of use
- Copyright holder:
- Informa UK Limited, trading as Taylor & Francis Group
- Copyright date:
- 2025
- Rights statement:
- © 2025 Informa UK Limited, trading as Taylor & Francis Group.
- Notes:
- The author accepted manuscript (AAM) of this paper has been made available under the University of Oxford's Open Access Publications Policy, and a CC BY public copyright licence has been applied.
- Licence:
- CC Attribution (CC BY)
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