Dissipation and criticality in the lowest Landau level of graphene

Jia, Xun; Goswami, Pallab; Chakravarty, Sudip

Dissipation and criticality in the lowest Landau level of graphene

Authors

Jia, Xun

Goswami, Pallab

Chakravarty, Sudip

Description

The lowest Landau level of graphene is studied numerically by considering a tight-binding Hamiltonian with disorder. The Hall conductance $σ_\mathrm{xy}$ and the longitudinal conductance $σ_\mathrm{xx}$ are computed. We demonstrate that bond disorder can produce a plateau-like feature centered at $ν=0$, 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 $\sim 7/3$.
4 pages, 5 figures