INTRODUCTION

Electron–electron interactions play an important role in shaping the behavior of quantum materials, often driving these systems into emergent phases that lie beyond the prediction of single-particle theories. When interactions are sufficiently strong, the collective dynamics of electrons can stabilize exotic states of matter, including unconventional superconducting states with nontrivial pairing mechanisms, Mott insulating states arising from interaction-induced localization, and topological phases characterized by fractionalized excitations [1–3]. These phenomena manifest as a direct consequence of the interplay between kinetic energy, Coulomb repulsion, and underlying lattice or band structure, leading to highly nontrivial many-body correlations. The profound theoretical and experimental implications posed by these systems—ranging from the breakdown of conventional Fermi-liquid descriptions to the emergence of long-range entanglement and novel quasiparticles—underscore why correlation physics remains a central and continuously evolving theme in condensed matter research [3,4].

The advent of moiré engineering in van der Waals heterostructures has opened a new frontier in the study of strongly correlated and topological quantum materials. By introducing a slight twist between two atomically thin layers, long-wavelength moiré superlattices emerge, giving rise to highly tunable electronic structures. These moiré patterns can drastically reshape the band dispersion, leading to flat bands that amplify electron–electron interactions and enable a wide range of emergent quantum phenomena. Recent progress has revealed a diverse landscape of novel quantum phenomena in moiré materials (Fig. 1). These include unconventional superconductivity, quantum phase transition, Chern insulators, orbital ferromagnets, fractional Chern insulators (FCI) and so on—all of which have markedly surpassed conventional theoretical paradigms [5–12]. Moiré systems offer a uniquely tunable platform for exploring correlated electronic phenomena, providing easier-to-access control over band filling, displacement field, and twist angle compared to traditional quantum materials.

Figure 1.: Schematic overview of quantum states that are associated with electronic correlation and topology in twisted graphene moiré superlattice. Superconductivity is depicted as being simultaneously intertwined with both correlation and topology.

Among the broader class of moiré systems, twisted graphene moiré superlattice stands out as the seminal platform that gave rise to the field of “twistronics.” Hosting a multicomponent subset of isospin flavors and nontrivial quantum geometry, twisted graphene systems exhibit rich and distinctive moiré flat-band physics that is intimately associated with the interplay of topology, electronic correlation, symmetry breaking and superconductivity.

This review is organized around three central concepts—twist, correlation and topology—and their interplay in influencing the emergent quantum phases, particularly superconductivity. From an experimental perspective, we are trying to cover a broad scope of moiré physics with a focus on magic-angle twisted bilayer graphene (MATBG). This review begins with a discussion on how the twist angle acts as a band-engineering knob to generate moiré flat bands with strongly suppressed kinetic energy in MATBG. We then examine the many-body reconstruction of these flat bands, highlighting flavor symmetry breaking, intervalley coherent order, and other interaction-driven phenomena revealed by advanced real-space, momentum-space, and thermodynamic probes. Next, we review the emergence of topological phases, including orbital Chern insulators, FCIs, and topological electronic crystals, arising from the interplay between electronic correlations and band topology. We further discuss the non-BardeenCooperSchrieffer (BCS) superconductivity in MATBG, emphasizing its strong-coupling nature, gap structure, and the role of quantum geometry in the superfluid response. The scope is then extended to twisted multilayer graphene systems, which exhibit enhanced tunability and new correlated behaviors. Finally, we outline key open questions and future directions concerning the microscopic origin of superconductivity and the exploration of novel quantum phases in twisted graphene systems.