Splitting of the zero-energy Landau level and universal dissipative conductivity at critical points in disordered graphene

We report on robust features of the longitudinal conductivity (σ_xx) of the graphene zero-energy Landau level in the presence of disorder and varying magnetic fields. By mixing an Anderson disorder potential with a low density of sublattice impurities, the transition from metallic to insulating states is theoretically explored as a function of Landau-level splitting, using highly efficient real-space methods to compute the Kubo conductivities (both σ_xx and Hall σ_xy). As long as valley degeneracy is maintained, the obtained critical conductivity σ_xx≃1.4e2/h is robust upon an increase in disorder (by almost 1 order of magnitude) and magnetic fields ranging from about 2 to 200 T. When the sublattice symmetry is broken, σ_xx eventually vanishes at the Dirac point owing to localization effects, whereas the critical conductivities of pseudospin-split states (dictating the width of a σ_xy=0 plateau) change to σ_xx≃e2/h, regardless of the splitting strength, superimposed disorder, or magnetic strength. These findings point towards the nondissipative nature of the quantum Hall effect in disordered graphene in the presence of Landau level splitting.