Structural, Electronic, and Optical Properties of Moiré Materials: A Computational Modeling Handbook

Moiré materials, formed by stacking layered materials with a lattice mismatch or twist, exhibit long-wavelength periodicities that qualitatively alter their electronic and optical properties, leading to emergent phenomena such as superconductivity, magnetism, and nonlinear optical responses. Modeling these effects is challenging because the underlying physics spans atomic to mesoscale dimensions and requires formalisms that explicitly treat electronic correlations. This review surveys computational methods for capturing these phenomena, highlighting first-principles approaches based on density functional and many-body perturbation theories and their connection to lower-scaling frameworks such as empirical, continuum, and machine-learning models. We outline the regimes each method addresses, key approximations for realistic systems, and emerging strategies for modeling structural, electronic, optical, and dynamical properties, as well as validation strategies given available experimental capabilities.