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Supersymmetry and Unconventional Quantum Hall Effect in Graphene | | Motohiko Ezawa
; | | Date: |
3 Jun 2006 | | Subject: | Mesoscopic Systems and Quantum Hall Effect | | 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 $sigma_{xy}=pm (2n+j_{uparrow}+j_{downarrow}) 2e^{2}/h$. | | Source: | arXiv, cond-mat/0606084 | | Services: | Forum | Review | PDF | Favorites | |
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