Supersymmetry and Correlated Electrons in Graphene Quantum Hall Effect

Details Supersymmetry and Correlated Electrons in Graphene Quantum Hall Effect Supersymmetry and Correlated Electrons in Graphene Quantum Hall Effect

2006-09-24

arxiv.org/abs/cond-mat/0609612v1

Physica E 40, 269 (2007)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

5 pages, 2 figures

Scientific paper

10.1016/j.physe.2007.06.038

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 $\nu =\pm (4n-2)$ for small magnetic field $B$ and at $\nu =0$, $\pm 1$, $\pm 2n$ for large $B$ with $n$ natural numbers.

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