Review of the tight-binding method applicable to the properties of moiré superlattices

XH Kuang and F Escudero and PA Pantaleon and F Guinea and Z Zhan, PHYSICAL CHEMISTRY CHEMICAL PHYSICS, 27, 25232-25253 (2025).

DOI: 10.1039/d5cp03472h

Moir & eacute; superlattices have emerged as a versatile platform for exploring a wide range of exotic quantum phenomena. Unlike angstrom- scale materials, the moir & eacute; 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 & eacute; materials. In this review, we provide a comprehensive overview of atomistic TB Hamiltonians and the numerical techniques commonly used to model graphene-based, TMD-based and hBN-based moir & eacute; superlattices. We also discuss the connection between atomistic TB descriptions and effective low-energy continuum models. Two examples of different moir & eacute; 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 & eacute; superlattices.

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