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Updated: Jan 11, 2026

Optimized Fabrication Procedure for High-Quality Graphene-based Moiré Superlattice Devices
Published on: July 11, 2025
Review of the tight-binding method applicable to the properties of moiré superlattices
Xueheng Kuang1, Federico Escudero2, Pierre A Pantaleón2
1Texas Materials Institute and Department of Mechanical Engineering, The University of Texas at Austin, Austin, Texas 78731, USA.
Abstract:
Moiré superlattices have emerged as a versatile platform for exploring a wide range of exotic quantum phenomena. Unlike angstrom-scale materials, the moiré 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 moiré 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 moiré superlattices. We also discuss the connection between atomistic TB descriptions and effective low-energy continuum models. Two examples of different moiré 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 moiré superlattices.
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