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

TL;DR

This study uses classical percolation models to analyze the quantum Hall transition in high-mobility 2D electron gases under weak magnetic fields, confirming some theoretical predictions and revealing new transition behaviors.

Contribution

It introduces a classical percolation approach to study the quantum Hall transition, extending understanding into very weak magnetic field regimes and inhomogeneity effects.

Findings

Transition occurs at _{xy}=1/2 for _{xx}10, matching quantum simulations.

Transition boundary follows _{xy} _{xx}^{0.5} for larger _{xx}.

Different percolation behavior observed in the strong inhomogeneity limit.

Abstract

We consider magnetotransport in high-mobility 2D electron gas in a non-quantizing 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 non-diagonal conductivity is equal to 1/2. The weaker is the magnetic field the harder it is to locate a delocalization transition using quantum simulations. The main idea of the present 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 to access the domain of very weak magnetic fields. Simulation results confirm the criterion \sigma_{xy}=1/2 for values \sigma_{xx}\sim 10, where they agree with earlier quantum simulation results. However for larger \sigma_{xx} we find that the transition boundary is described by \sigma_{xy} \sigma_{xx}^k with k= 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 \sigma_{xy} \sigma_{xx}^{0.6}.