Supersymmetry and Correlated Electrons in Graphene Quantum Hall Effect

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We present a supersymmetric description of the quantum Hall effect (QHE) in graphene. The noninteracting system is supersymmetric separately at the so-called K and K' points of the Brillouin zone corners. Its essential consequence is that the energy levels and the Landau levels are different objects in graphene QHE. Each energy level has a four-fold degeneracy within the noninteracting theory. With the Coulomb interaction included, an excitonic gap opens in the zero-energy state, while each nonzero energy level splits into two levels since up-spin and down-spin electrons come from different Landau levels. We argue the emergence of the plateaux at ν=± (4n-2) for small magnetic field B and at ν=0, ± 1, ± 2n for large B with n natural numbers.