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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.13114 |
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Table of Contents:
- Lattice relaxation profoundly reshapes electronic structures in twisted materials. Prevailing treatments, however, typically rely on large-scale density functional theory (DFT), which is computationally costly and mechanistically opaque. Here, we develop a unified analytical framework to overcome these limitations. From continuum elastic theory, we derive closed-form solutions for both in-plane and out-of-plane relaxation fields. We further introduce an analytical phase factor expansion theory that maps relaxation into the electronic Hamiltonian. By applying this framework, the relaxation-mediated single-particle and many-body topological phase transitions in twisted MoTe$_{2}$ is accurately captured, and the evolution of flat bands in magic-angle graphene is quantitatively reproduced. Our work transforms the research of moiré relaxation from black-box numerical fitting to an analytical paradigm, offering fundamental insights, exceptional efficiency, and general applicability to a wide range of twisted materials.