Fluctuating Hall resistance defeats the quantized Hall insulator

TL;DR

This study uses a simplified network model to analyze the transition from quantum Hall plateau to insulator, revealing that quantum coherence causes fluctuating Hall resistance that challenges the notion of a stable quantized Hall insulator.

Contribution

It demonstrates how quantum coherence affects Hall resistance fluctuations and the conditions under which a quantized Hall insulator can be observed or transitions to diverging resistance.

Findings

Quantized Hall insulator observed up to R_L ~25 h/e^2

Hall resistance diverges as R_L increases beyond this point

Crossover depends on averaging procedure used in analysis

Abstract

Using the Chalker-Coddington network model as a drastically simplified, but universal model of integer quantum Hall physics, we investigate the plateau-to-insulator transition at strong magnetic field by means of a real-space renormalization approach. Our results suggest that for a fully quantum coherent situation, the quantized Hall insulator with R_H approx. h/e^2 is observed up to R_L ~25 h/e^2 when studying the most probable value of the distribution function P(R_H). Upon further increasing R_L ->\infty the Hall insulator with diverging Hall resistance R_H \propto R_L^kappa is seen. The crossover between these two regimes depends on the precise nature of the averaging procedure.