Reflection Symmetry and Quantized Hall Resistivity near Quantum Hall Transition

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 ${\rho }_{xx}$.

3 pages, 4 figures; figure 4 is replaced

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• Semicircle: An exact relation in the Integer and Fractional Quantum Hall Effect
• Phase Diagram of Integer Quantum Hall Effect
• Quantum criticality at the Chern-to-normal insulator transition
• Emergence of integer quantum Hall effect from chaos
• Quantum Breakdown of the Quantized Hall Insulator
• Characterization of the Quantized Hall Insulator Phase in the Quantum Critical Regime
• The scaling behavior of the insulator to plateau transition in topological band model
• The Quantized Hall Insulator: a "Quantum" Signature of a "Classical" Transport Regime?
• Universal scaling, beta function, and metal-insulator transitions