Aspects of the Fractional Quantum Hall Effect in Graphene

Abstract

We present a brief overview of the nature of the fractional quantum Hall effect (FQHE) in monolayer and bilayer graphene. After a short introduction on the effect and the pseudopotential description of interacting electrons in the quantum Hall regime, we discuss in detail the magnetic field effects on electrons in monolayer graphene. We also briefly discuss the experimental signatures of the effect reported in the literature. In bilayer graphene, the effect manifests itself in a very different manner and we discuss in detail the various novel effects one expects there due to electron-electron interactions. The nature of the collective excitations of Dirac fermions in trilayer graphene is also briefly discussed. Existence of some exotic states in bilayer graphene, such as the Pfaffian state is also highlighted. Finally, we have touched upon the properties of the FQHE states of Dirac fermions on the surface of a topological insulator.