Phase diagram of the weak-magnetic-field quantum Hall transition quantified from classical percolation

We consider magnetotransport in high-mobility two-dimensional electron gas σ_xx≫1 in a nonquantizing magnetic field. We employ a weakly chiral network model to test numerically the prediction of the scaling theory that the transition from an Anderson to a quantum Hall insulator takes place when the Drude value of the nondiagonal conductivity σ_xy is equal to 1/2 (in the units of e²/h). The weaker the magnetic field, the harder it is to locate a delocalization transition using quantum simulations. The main idea of this study is that the position of the transition does not change when a strong local inhomogeneity is introduced. Since the strong inhomogeneity suppresses interference, transport reduces to classical percolation. We show that the corresponding percolation problem is bond percolation over two sublattices coupled to each other by random bonds. Simulation of this percolation allows us to access the domain of very weak magnetic fields. Simulation results confirm the criterion σ_xy=1/2 for values σ_xx∼10, where they agree with earlier quantum simulation results. However, for larger σ_xx, we find that the transition boundary is described by σ_xy∼σ_xx^κ with κ≈0.5, i.e., the transition takes place at higher magnetic fields. The strong inhomogeneity limit of magnetotransport in the presence of a random magnetic field, pertinent to composite fermions, corresponds to a different percolation problem. In this limit, we find for the delocalization transition boundary σ_xy∼σ_xx^0.6.