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

Abstract

Dynamical scaling of the optical Hall conductivity σxy(εF, 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, σxy(εF, 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 σxy(εF, ω) in the honeycomb lattice model with bond disorder (preserving chiral symmetry), becomes anomalous.