Supersymmetry and unconventional quantum Hall effect in monolayer, bilayer and trilayer graphene

We present a unified description of the quantum Hall effect in monolayer, bilayer and trilayer graphene based on the supersymmetric formalism. The key property is that the Zeeman splitting is exactly as large as the Landau level separation for Dirac electrons. It follows that the zero-energy state emerges and that the nonzero-energy states make a supermultiplet made of the up-spin and down-spin states coming from different Landau levels. Analyzing Coulomb effects on the nonzero-energy states, we derive a remarkable result that the effective Coulomb potential depends on spins in each energy level.