Dissipation and criticality in the lowest Landau level of graphene

Details Dissipation and criticality in the lowest Landau level of graphene Dissipation and criticality in the lowest Landau level of graphene

2008-04-11

arxiv.org/abs/0804.1975v1

Phys. Rev. Lett. 101, 036805 (2008)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages, 5 figures

Scientific paper

10.1103/PhysRevLett.101.036805

The lowest Landau level of graphene is studied numerically by considering a tight-binding Hamiltonian with disorder. The Hall conductance $\sigma_\mathrm{xy}$ and the longitudinal conductance $\sigma_\mathrm{xx}$ are computed. We demonstrate that bond disorder can produce a plateau-like feature centered at $\nu=0$, while the longitudinal conductance is nonzero in the same region, reflecting a band of extended states between $\pm E_{c}$, whose magnitude depends on the disorder strength. The critical exponent corresponding to the localization length at the edges of this band is found to be $2.47\pm 0.04$. When both bond disorder and a finite mass term exist the localization length exponent varies continuously between $\sim 1.0$ and $\sim 7/3$.

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