Abstract
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.
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