Anomalous criticality in the quantum Hall transition at $n=0$ Landau level of graphene with chiral-symmetric disorders

Abstract

We investigate numerically whether the chiral symmetry is the sole factor dominating the criticality of the quantum Hall transitions in disordered graphene. When the disorder respects the chiral symmetry, the plateau-to-plateau transition at the $n=0$ Landau level is shown to become anomalous (i.e., step-function-like). Surprisingly, however, the anomaly is robust against the inclusion of the uniform next-nearest neighbor hopping, which degrades the chiral symmetry of the lattice models. We have also shown that the ac (optical) Hall conductivity exhibits a robust plateau structure when the disorder respects the chiral symmetry.

8 pages, 10 figures

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• Lattice realization of the generalized chiral symmetry in two dimensions
• Topologically protected Landau levels in bilayer graphene in finite electric fields
• Robust Zero Modes in Disordered Two-Dimensional Honeycomb Lattice with Kekulé Bond Ordering
• Chiral Symmetry and Electron-Electron Interaction in Many-Body Gap Formation in Graphene