Splitting of the quantum Hall transition in disordered graphenes

Abstract

Integer quantum Hall effect is studied for a noninteracting electron in a monolayer graphene. We calculate the Hall conductivity within a single Landau level in the presence of randomness in the bond couplings and in the on-site potential, and estimate the critical energies for the quantum Hall transition. We show that valley-degenerated ($K$ and $K^{\prime }$ points) Landau levels contain two displaced critical energies indicating that an extra Hall plateau appears inside, while the localization is found to be much stronger in the Landau level $N=0$ than in $N=1$.