Theoretical aspects of the fractional quantum Hall effect in graphene

We review the theoretical basis and understanding of electronic interactions in graphene Landau levels (LLs) in the limit of strong correlations. This limit occurs when inter-LL excitations may be omitted because they belong to a high-energy sector, whereas the low-energy excitations only involve the same level, such that the kinetic energy (of the LL) is an unimportant constant. Two prominent effects emerge in this limit of strong electronic correlations: generalized quantum Hall ferromagnetic states that profit from the approximate fourfold spin-valley degeneracy of graphene's LLs and the fractional quantum Hall effect. Here, we discuss these effects in the framework of an SU(4)-symmetric theory, in comparison with available experimental observations.