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

Tohru Kawarabayashi, Takahiro Morimoto, Yasuhiro Hatsugai, Hideo Aoki

Published 2010-08-16Version 1

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.