Emergent phases in graphene flat bands

Abstract: Electronic correlations in two-dimensional materials play a crucial role in stabilising emergent phases of matter. The realisation of correlation-driven phenomena in graphene has remained a longstanding goal, primarily due to the absence of strong electron-electron interactions within its low-energy bands. In this context, magic-angle twisted bilayer graphene has recently emerged as a novel platform featuring correlated phases favoured by the low-energy flat bands of the underlying moir\'e superlattice. Notably, the observation of correlated insulators and superconductivity has garnered significant attention, leading to substantial progress in theoretical and experimental studies aiming to elucidate the origin and interplay between these two phases. A wealth of correlated phases with unprecedented tunability was discovered subsequently, including orbital ferromagnetism, Chern insulators, strange metallicity, density waves, and nematicity. However, a comprehensive understanding of these closely competing phases remains elusive. The ability to controllably twist and stack multiple graphene layers has enabled the creation of a whole new family of moir\'e superlattices with myriad properties being discovered at a fast pace. Here, we review the progress and development achieved so far, encompassing the rich phase diagrams offered by these graphene-based moir\'e systems. Additionally, we discuss multiple phases recently observed in non-moir\'e multilayer graphene systems. Finally, we outline future opportunities and challenges for the exploration of hidden phases in this new generation of moir\'e materials.