Supersymmetry and Unconventional Quantum Hall Effect in Graphene

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We present a unified description of the quantum Hall effect in graphene on the basis of the 8-component Dirac Hamiltonian and the supersymmetric (SUSY) quantum mechanics. It is remarkable that the zero-energy state emerges because the Zeeman splitting is exactly as large as the Landau level separation, as implies that the SUSY is a good symmetry. For nonzero energy states, the up-spin state and the down-spin state form a supermultiplet possessing the spin SU(2) symmetry. We extend the Dirac Hamiltonian to include two indices j and j, characterized by the dispersion relation E(p) ∝ pj+j and the Berry phase π(j-j). The quantized Hall conductivity is shown to be σxy=± (2n+j+j) 2e²/h.