Dynamical scaling analysis of the optical Hall conductivity in the graphene quantum Hall system with various types of disorder

Dynamical scaling of the optical Hall conductivity σ _xy(ε_F, ω) at the n = 0 Landau level in graphene is analyzed for the 2D effective Dirac fermion and honeycomb lattice models with various types of disorder. In the Dirac fermion model with potential disorder, σ_xy(ε_F, ω) obeys a well-defined dynamical scaling, characterized by the localization exponent ν and the dynamical critical exponent z. In sharp distinction, scaling behavior of σ_xy(ε_F, ω) in the honeycomb lattice model with bond disorder (preserving chiral symmetry), becomes anomalous.