Reflection Symmetry and Quantized Hall Resistivity near Quantum Hall Transition

TL;DR

This paper provides numerical evidence that reflection symmetry of resistivities and quantized Hall resistivity occur near the quantum Hall transition, driven by universal conductance scaling, consistent with recent experimental findings.

Contribution

It demonstrates that conductance scaling governs resistivity symmetry and quantization near the quantum Hall transition, independent of particle-hole symmetry.

Findings

Reflection symmetry of resistivities near transition

Quantization of Hall resistivity at transition

Deviation of resistivity from quantization in insulating phase

Abstract

We present a direct numerical evidence for reflection symmetry of longitudinal resistivity $\rho_{xx}$ and quantized Hall resistivity $\rho_{xy}$ near the transition between $\nu=1$ quantum Hall state and insulator, in accord with the recent experiments. Our results show that a universal scaling behavior of conductances, $\sigma_{xx}$ and $\sigma_{xy}$, in the transition regime decide the reflection symmetry of $\rho_{xx}$ and quantization of $\rho_{xy}$, independent of particle-hole symmetry. We also find that in insulating phase away from the transition region $\rho_{xy}$ deviates from the quantization and diverges with $\rho_{xx}$.