The Quantized Hall Insulator: a "Quantum" Signature of a "Classical" Transport Regime?

TL;DR

This paper reviews experimental and theoretical studies on the quantized Hall insulator phenomenon, highlighting the role of incoherent transport in maintaining quantization and discussing the impact of quantum coherence and localization.

Contribution

It introduces a model of the insulator as a network of QH puddles that explains quantized Hall resistivity under incoherent transport conditions.

Findings

Quantized Hall resistivity is robust in incoherent transport models.

Quantum coherence leads to localization, destroying the quantized Hall insulator.

Localization length shorter than dephasing length causes divergence in Hall resistivity.

Abstract

Experimental studies of the transitions from a primary quantum Hall (QH) liquid at filling factor 1/k (with k an odd integer) to the insulator have indicated a ``quantized Hall insulator'' (QHI) behavior: while the longitudinal resistivity diverges with decreasing temperature and current bias, the Hall resistivity remains quantized at the value $k h/ e^2$. We review the experimental results and the theoretical studies addressing this phenomenon. In particular, we discuss a theoretical approach which employs a model of the insulator as a random network of weakly coupled puddles of QH liquid at fixed filling factor. This model is proved to exhibit a robust quantization of the Hall resistivity, provided the electron transport on the network is INCOHERENT. Subsequent theoretical studies have focused on the controversy whether the assumption of incoherence is necessary. The emergent conclusion is that in the quantum coherent transport regime, quantum interference destroys the QHI as a consequence of localization. Once the localization length becomes much shorter than the dephasing length, the Hall resistivity diverges. We conclude by mentioning some recent experimental observations and open questions.