Moiré effects in low-dimensional heterostructures: from 2D materials to 2D-3D mixed-dimensional systems

Moiré superlattices provide a versatile means of modifying electronic bands through periodic potentials generated by lattice mismatch or rotational misalignment. Over the past decade, this concept has reshaped the study of low-dimensional quantum materials, enabling the observation of flat bands, correlated insulating behavior, unconventional superconductivity, excitonic states, and topological responses. More recently, moiré physics has begun to move beyond the conventional limit of atomically thin two-dimensional (2D) heterostructures. Experimental studies have shown that a moiré potential formed at a 2D interface can propagate into adjacent three-dimensional materials and reconstruct their bulk electronic states, giving rise to mixed-dimensional moiré systems. This review summarizes recent progress in moiré effects from 2D platforms to mixed-dimensional architectures. We first present the fundamental physical definition of moiré patterns and trace their historical development. We then review graphene-based moiré systems with different layer numbers, where twist-angle control modifies band dispersion, enhances electronic correlations, and leads to superconductivity near magic angles. The discussion is extended to transition metal dichalcogenide moiré heterostructures, with emphasis on excitonic physics, interlayer hybridization, correlation effects, and nontrivial band topology. We then focus on 2D-3D mixed-dimensional heterostructures, where interfacial moiré modulation penetrates into bulk materials and produces electronic reconstruction beyond the interface. Finally, we discuss future directions involving broader material choices, improved control over stacking and twist geometry, advanced probes of buried moiré potentials, and the search for unexplored correlated and topological phases.