Supersymmetry and Unconventional Quantum Hall Effect in Graphene

Abstract

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 $j_{\uparrow }$ and $j_{\downarrow }$, characterized by the dispersion relation $E(p)\propto p^{j_{\uparrow }+j_{\downarrow }}$ and the Berry phase $\pi (j_{\uparrow }-j_{\downarrow })$. The quantized Hall conductivity is shown to be ${\sigma }_{xy}=\pm (2n+j_{\uparrow }+j_{\downarrow })2e^2/h$.

5 pages, 2 figures

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