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Mean-field modeling of moiré materials: a user's guide with selected applications to twisted bilayer graphene
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DOI：10.1080/00018732.2025.2600658.png)
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Abstract
En 中文
We review the theoretical modeling of moir & eacute; 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 moir & eacute; 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 moir & eacute; superlattice are exactly captured by mean-field ans & auml;tze. We then illustrate the phenomenological shortcomings of this limit, leading us naturally into a discussion of the intermediate-coupling incommensurate Kekul & eacute; 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 moir & eacute; systems.
Keywords:
moir & eacute
materials
twisted bilayer graphene
strongly correlated electrons
Hartree-Fock techniques
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