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arXiv · 2511.04899

Review of the tight-binding method applicable to the properties of moir\'e superlattices

Xueheng Kuang·Federico Escudero·Pierre A. Pantaleón·Francisco Guinea·Zhen Zhan
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Abstract

Moir\'e superlattices have emerged as a versatile platform for exploring a wide range of ex- otic quantum phenomena. Unlike angstrom-scale materials, the moir\'e length-scale system contains a large number of atoms, and its electronic structure is significantly modulated by the lattice relaxation. These features pose a huge theoretical challenge. Among the available theoretical approaches, tight-binding (TB) methods are widely employed to predict the electronic, transport, and optical properties of systems such as twisted graphene, twisted transition-metal dichalcogenides (TMDs), and related moir\'e materials. In this review, we pro- vide a comprehensive overview of atomistic TB Hamiltonians and the numerical techniques commonly used to model graphene-based, TMD-based and hBN-based moir\'e superlattices. We also discuss the connection between atomistic TB descriptions and effective low-energy continuum models. Two examples of different moir\'e materials and geometries are provided to emphasize the advantages of the TB methods. This review is intended to serve as a theoretical and practical guide for those seeking to apply TB methods to the study of various properties of moir\'e superlattices.

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Xueheng Kuang, Federico Escudero, Pierre A. Pantaleón, Francisco Guinea, Zhen Zhan. 2025-11-07. Review of the tight-binding method applicable to the properties of moir\'e superlattices. https://doi.org/10.1039/d5cp03472h

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