Superconductivity and charge density waves in graphene-based materials

Graphene-based materials have emerged as a versatile platform for exploring strongly correlated quantum phenomena, particularly superconductivity (SC) and charge density waves (CDWs), owing to their highly tunable electronic structure, reduced dimensionality, and sensitivity to external perturbations. While pristine monolayer graphene is not intrinsically superconducting and exhibits limited propensity toward charge ordering, a variety of engineered graphene systems have demonstrated remarkable SC and CDW phases through mechanisms involving doping, intercalation, proximity coupling, strain, and moiré superlattice engineering. The discovery of correlated insulating states and superconductivity in magic-angle twisted bilayer graphene has revolutionized the field by revealing unprecedented opportunities for studying unconventional pairing mechanisms and competing electronic orders in a purely carbon-based material platform. This review critically examines the current understanding of emergent SC and CDW in graphene-derived systems. We survey the diverse classes of graphene-based superconductors, including chemically doped and intercalated graphene, twisted bi- and trilayer graphene structures, and proximity-induced superconducting heterostructures, emphasizing the role of electron-phonon coupling, flat-band formation, and interfacial effects. Subsequently, we discuss the fundamental origins of CDW formation in graphene, focusing on electron-phonon interactions, Peierls instability, Fermi-surface nesting, defect engineering, doping, heterostructure design, and moiré-induced electronic reconstruction. The coexistence and competition between SC and charge-ordered phases, as revealed by scanning tunneling microscopy (STM), angle-resolved photoemission spectroscopy (ARPES), transport measurements, and other advanced experimental techniques are discussed. This review analyzes the principal theoretical frameworks employed to describe these correlated states, including the Holstein model, Eliashberg theory, unconventional pairing scenarios, strain-induced gauge fields, and topological superconductivity. We assess the extent to which conventional electron-phonon-mediated mechanisms can account for experimental observations and discuss alternative strongly correlated and topological descriptions. By integrating experimental discoveries with theoretical developments, this review outlines future directions for both fundamental research and quantum-device applications. .