Dissipation and criticality in the lowest Landau level of graphene

Abstract

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 $\sim 7/3$.

4 pages, 5 figures

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• Edge states in graphene in magnetic fields -- a speciality of the edge mode embedded in the n=0 Landau band
• Quantum transport in chemically functionalized graphene at high magnetic field: Defect-Induced Critical States and Breakdown of Electron-Hole Symmetry
• Quantum oscillations in graphene in the presence of disorder and interactions