Fractional quantum Hall effect (FQHE) discovered experimentally in 1982 is still mysterious, not fully understood phenomenon. It fundaments are linked with a nontrivial topological effects in 2D space going beyond the standard description of FQHE with local quantum mechanics. The study of integer and fractional QHE in graphene might be helpful in resolution of this fundamental problem in many body quantum physics. FQHE has been observed both in monolayer and bilayer graphene with an exceptional accuracy due to advances in experimental techniques and purity of graphene samples. Recent experimental observations of FQHE in the bilayer graphene reveal different FQHE behavior than in the monolayer samples or in conventional semiconductor 2D materials. This unexpected phenomena related to Hall physics in the bilayer systems allows to better understand more than 30 years old puzzle of FQHE. In the chapter we will summarize the recent and controversial experimental observations of FQHE in bilayer graphene and describe the topology foundations which may explain the oddness of correlated multiparticle states in the bilayer system. These topological arguments shed also a new light on understanding of heuristic CF concept for FQHE and deeper the topological sense of the famous Laughlin function describing this strongly correlated state.
Part of the book: Graphene Materials