Hall Resistivity and Dephasing in the Quantum Hall Insulator

TL;DR

This paper investigates the behavior of Hall resistivity in the quantum Hall insulator phase, revealing how it scales with dephasing length and proposing a new way to probe dephasing experimentally.

Contribution

It introduces a model incorporating finite dephasing length into the Hall insulator, showing how resistivity scales and remains quantized under different regimes.

Findings

Hall resistivity scales with longitudinal resistivity in the quantum coherent regime

Resistivities diverge exponentially with dephasing length

Resistivity remains quantized in the Ohmic limit regardless of longitudinal resistivity

Abstract

The longstanding problem of the Hall resistivity rho(x,y) in the Hall insulator phase is addressed using four-lead Chalker-Coddington networks. Electron interaction effects are introduced via a finite dephasing length. In the quantum coherent regime, we find that rho(x,y) scales with the longitudinal resistivity rho(x,x), and they both diverge exponentially with dephasing length. In the Ohmic limit, (dephasing length shorter than Hall puddles' size), rho(x,y) remains quantized and independent of rho(x,x). This suggests a new experimental probe for dephasing processes.